Accuracy and Stability of Numerical Algorithms
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Publication:4779477
DOI10.1137/1.9780898718027zbMath1011.65010OpenAlexW2020804487WikidataQ47672713 ScholiaQ47672713MaRDI QIDQ4779477
Publication date: 27 November 2002
Full work available at URL: http://eprints.maths.manchester.ac.uk/238/4/asna2_cover.pdf
softwareNewton's methodbibliographytextbookbackward error analysisforward error analysistest matricesLAPACKfinite precision computation
Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Roundoff error (65G50) Software, source code, etc. for problems pertaining to linear algebra (15-04) Numerical linear algebra (65Fxx)
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A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges, Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems, Condition numbers and backward perturbation bound for linear matrix equations, Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations, Tight and efficient enclosure of matrix multiplication by using optimized BLAS, Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction, Backward stability with almost strictly sign regular matrices, Perturbation analysis for the periodic generalized coupled Sylvester equation, An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments, The Bunch-Kaufman factorization of symmetric matrices signature similar to sign regular matrices, A Bessel collocation method for numerical solution of generalized pantograph equations, Aggregation based on graph matching and inexact coarse grid solve for algebraic two grid, Shifted L-BFGS systems, Running error for the evaluation of rational Bézier surfaces, Barycentric-Remez algorithms for best polynomial approximation in the chebfun system, Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin's \(\sin (\theta)\) theorem, Verified numerical computations for large-scale linear systems., Perturbation analysis for the symplectic QR factorization, On the ordering of credibility factors, A stable parallel algorithm for block tridiagonal Toeplitz-block-Toeplitz linear systems, Beyond linear subspace clustering: a comparative study of nonlinear manifold clustering algorithms, Condition numbers of the minimum norm least squares solution for the least squares problem involving Kronecker products, On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots, Calculating a function of a matrix with a real spectrum, Anymatrix: an extensible MATLAB matrix collection, Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations, Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method, Imposing symmetry in augmented linear systems, The dynamical functional particle method for multi-term linear matrix equations, A division-free algorithm for numerically evaluating the determinant of a specific quasi-tridiagonal matrix, Error bounds on complex floating-point multiplication with an FMA, Iterative refinement of Schur decompositions, Computing Gaussian quadrature rules with high relative accuracy, Detection and correction of silent errors in the conjugate gradient algorithm, Error‐free transformation of matrix multiplication with a posteriori validation, Balanced incomplete factorization preconditioner with pivoting, On the stability of Filon-Clenshaw-Curtis rules, Kernel regression analysis of tie-breaker designs, Singular quadratic eigenvalue problems: linearization and weak condition numbers, Structural backward stability in rational eigenvalue problems solved via block Kronecker linearizations, Embedded MPC Controller Based on Interior-Point Method with Convergence Depth Control, Error bounds and a condition number for the absolute value equations, Jordan-Schur algorithms for computing the matrix exponential, Matrix Structures in Queuing Models, \textit{TimeEvolver}: a program for time evolution with improved error bound, The equivalence of the constrained Rayleigh quotient and Newton methods for matrix polynomials expressed in different polynomial bases along with the confluent case, A generalization of the Bott-Duffin inverse and its applications, Computing the conditioning of the components of a linear least-squares solution, Backward perturbation analysis for scaled total least-squares problems, The growth factor of a Hadamard matrix of order 16 is 16, Rounding error analysis of the classical Gram-Schmidt orthogonalization process, On perturbation bounds of Kronecker product linear systems and their level-2 condition numbers, The numerical condition of univariate and bivariate degree elevated Bernstein polynomials, Condition numbers for structured least squares problems, Unnamed Item, Algorithms for the matrix \(p\)th root, Verification of positive definiteness, Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials, Scaled and Squared Subdiagonal Padé Approximation for the Matrix Exponential, Numerical Instability of Resultant Methods for Multidimensional Rootfinding, Perturbation analysis for the matrix least squares problem \(A X B = C\), Robust eigenstructure clustering by non-smooth optimisation, Perturbation analysis of a quadratic matrix equation associated with an \(M\)-matrix, Computing the common zeros of two bivariate functions via Bézout resultants, Backward error analysis of the extended iterative refinement or improvement algorithm for solving ill conditioned linear system, Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block, The Inverse Eigenvector Problem for Real Tridiagonal Matrices, Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities, A symmetric linear system solver, Perturbation analysis for a class of fuzzy linear systems, Some Sets of Relative Stability Under Perturbations of Branched Continued Fractions with Complex Elements and a Variable Number of Branches, Numerical validation of compensated summation algorithms with stochastic arithmetic, Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension, Convergence acceleration of modified Fourier series in one or more dimensions, Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures, Principal Pivot Transforms of Quasidefinite Matrices and Semidefinite Lagrangian Subspaces, Projection methods for large-scale T-Sylvester equations, Factorized Approximate Inverses with Adaptive Dropping, Solving Generalized CDT Problems via Two-Parameter Eigenvalues, On the Stability of Some Hierarchical Rank Structured Matrix Algorithms, Improving the Numerical Stability of Fast Matrix Multiplication, Efficient Calculations of Faithfully Rounded l 2 -Norms of n -Vectors, Estimating the Largest Elements of a Matrix, On the Description and Stability of Orthogonal Transformations of Rank Structured Matrices, On parametrization of totally nonpositive matrices and applications, Stability and sensitivity of tridiagonal LU factorization without pivoting, Stable Computation of Generalized Matrix Functions via Polynomial Interpolation, Low-Rank Matrix Approximations Do Not Need a Singular Value Gap, Convergence analysis of accurate inverse Cholesky factorization, Accelerated multiple precision matrix multiplication using Strassen's algorithm and Winograd's variant, A fast and efficient algorithm for solving ill-conditioned linear systems, Hybrid solvers for composition and splitting methods, Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product, Scaling and modified squaring method for the matrix exponential, A note on the componentwise perturbation bounds of matrix inverse and linear systems, Line segment intersection testing, Solving SDGE models: a new algorithm for the Sylvester equation, Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs, Backward error and condition number analysis for the indefinite linear least squares problem, High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation, Data-Driven Balancing of Linear Dynamical Systems, Turing Pattern Dynamics in an SI Epidemic Model with Superdiffusion, Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation, Backward errors and small-sample condition estimation for ⋆-Sylveter equations, Computing the Signed Distance Between Overlapping Ellipsoids, Self-interacting dark matter in cosmology: accurate numerical implementation and observational constraints, Tuning Symplectic Integrators is Easy and Worthwhile, The Numerical Stability Analysis of Pipelined Conjugate Gradient Methods: Historical Context and Methodology, General Strong Polarization, First steps towards more numerical reproducibility, Solving Rank-Structured Sylvester and Lyapunov Equations, Randomized Complete Pivoting for Solving Symmetric Indefinite Linear Systems, Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C, Efficient approximation of random fields for numerical applications, An inexact shift‐and‐invert Arnoldi algorithm for Toeplitz matrix exponential, Finite difference weights, spectral differentiation, and superconvergence, Sensitivity analysis for the generalized Cholesky block downdating problem, Fourth- and Higher-order Interface Tracking Via Mapping and Adjusting Regular Semianalytic sets Represented by Cubic Splines, A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation, Exactly Solving Sparse Rational Linear Systems via Roundoff-Error-Free Cholesky Factorizations, Mixed Precision Recursive Block Diagonalization for Bivariate Functions of Matrices, Structured backward errors for two kinds of generalized saddle point systems, On Efficiently Computing the Eigenvalues of Limited-Memory Quasi-Newton Matrices, An explicit formula for the inverse of a factorial Hankel matrix, Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials, Finding the roots of a non-linear equation: history and reliability, Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case, Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization, Rational Minimax Approximation via Adaptive Barycentric Representations, Fast and Backward Stable Computation of Roots of Polynomials, Part II: Backward Error Analysis; Companion Matrix and Companion Pencil, A Householder-Based Algorithm for Hessenberg-Triangular Reduction, On the Symmetric Componentwise Relative Backward Error for Linear Systems of Equations, Incomplete LU Preconditioner Based on Max-Plus Approximation of LU Factorization, Level-2 condition numbers for least-squares solution of Kronecker product linear systems, A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems, Time Complexity and Convergence Analysis of Domain Theoretic Picard Method, On relative errors of floating-point operations: Optimal bounds and applications, Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector, Composite norms and perfect conditioning, Numerical solution of linear eigenvalue problems, Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions, Fast matrix multiplication and its algebraic neighbourhood, On Multivariate Interpolation, Numerical Analysis of Novel Finite Difference Methods, Error Analysis of TT-Format Tensor Algorithms, Low-Rank Updates and a Divide-And-Conquer Method for Linear Matrix Equations, Automatic Exploration of Reduced Floating-Point Representations in Iterative Methods, On Computing the Total Variation Distance of Hidden Markov Models., Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores, Accurate Computations and Applications of Some Classes of Matrices, Introduction to Communication Avoiding Algorithms for Direct Methods of Factorization in Linear Algebra, Strong-stability-preserving additive linear multistep methods, Numerical modular symbols for elliptic curves, A condition analysis of the weighted linear least squares problem using dual norms, Extended version with the analysis of dynamic system for iterative refinement of solution, Unnamed Item, Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations, A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation, On the numerical evaluation of Fredholm determinants, Perturbation analysis for the generalized Schur complement of a positive semi‐definite matrix, On growth factors of the modified Gram-Schmidt algorithm, A note on backward errors for structured linear systems, A pivoting strategy for symmetric tridiagonal matrices, Rigorous and Efficient Short Lattice Vectors Enumeration, Sharp estimates for perturbation errors in summations, Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization, Inexact Half-Quadratic Optimization for Linear Inverse Problems, Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization, Interpreting linear systems of equalities and inequalities. Application to the water supply problem, Enclosing Chebyshev Expansions in Linear Time, Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems, The Stability of Block Variants of Classical Gram--Schmidt, A Multiprecision Derivative-Free Schur--Parlett Algorithm for Computing Matrix Functions, On the condition number theory of the equality constrained indefinite least squares problem, Technical Note—A Robust Perspective on Transaction Costs in Portfolio Optimization, Selected Implementation Issues in Computation of the Grünwald-Letnikov Fractional-Order Difference by Means of Embedded System, Simultaneous tridiagonalization of two symmetric matrices, A note on backward errors for Toeplitz systems, On Frobenius normwise condition numbers for Moore–Penrose inverse and linear least-squares problems, A note on the solution of not balanced banded Toeplitz systems, An efficient linear programming solver for optimal filter synthesis, Accurate and efficient matrix exponential computation, Sign consistent linear programming problems, Parallel Prony's Method with Multivariate Matrix Pencil Approach and Its Numerical Aspects, Rethinking arithmetic for deep neural networks, Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations, Unnamed Item, Unnamed Item, Algebraic Error Analysis for Mixed-Precision Multigrid Solvers, Rank-Structured QR for Chebyshev Rootfinding, How Many Steps Still Left to $x$*?, Unnamed Item, On the probability distribution of condition numbers of complete intersection varieties and the average radius of convergence of Newton's method in the underdetermined case, Error bounds on complex floating-point multiplication, Interpolatory Methods for Generic BizJet Gust Load Alleviation Function, Gaussian Process Landmarking on Manifolds, Twice Is Enough for Dangerous Eigenvalues, Sensitivity analysis for the block Cholesky downdating problem, Computational and sensitivity aspects of eigenvalue-based methods for the large-scale trust-region subproblem, Unnamed Item, Optimizing and Factorizing the Wilson Matrix, Condition numbers of the least squares problems with multiple right-hand sides, Stability of QR-based fast system solvers for a subclass of quasiseparable rank one matrices, Further analysis of Kahan’s algorithm for the accurate computation of $2\times 2$ determinants, Extending the Scope of Robust Quadratic Optimization, On equal-input and monotone Markov matrices, The comparison of the estimators of banded toeplitz covariance structure under the high-dimensional multivariate model, Inf-sup stability implies quasi-orthogonality, Cross-Interactive Residual Smoothing for Global and Block Lanczos-Type Solvers for Linear Systems with Multiple Right-Hand Sides, A Note on Inexact Inner Products in GMRES, Hadamard Matrices: Insights into Their Growth Factor and Determinant Computations, The Short-Term Rational Lanczos Method and Applications, Semi-Infinite Programming using High-Degree Polynomial Interpolants and Semidefinite Programming, The Block Rational Arnoldi Method, A Class of Fast and Accurate Summation Algorithms, Eight Perspectives on the Exponentially Ill-Conditioned Equation $\varepsilon y - x y' + y = 0$, On computing the density of integers of the form $2^n+p$, A Class of Approximate Inverse Preconditioners Based on Krylov-Subspace Methods for Large-Scale Nonconvex Optimization, Multipreconditioned Gmres for Shifted Systems, Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method, Bayesian principal component regression with data-driven component selection, Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods, Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs, Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data, Robust attitude tracking control for a rigid spacecraft under input delays and actuator errors, Derivation and Analysis of Fast Bilinear Algorithms for Convolution, A geometric approach to subspace updates and orthogonal matrix decompositions under rank-one modifications, An optimal preconditioner for tensor equations involving Einstein product, Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade, On Iterative Solution of the Extended Normal Equations, Computing Enclosures for the Matrix Exponential, Probabilistic Error Analysis for Inner Products, On Soft Errors in the Conjugate Gradient Method: Sensitivity and Robust Numerical Detection, On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products, Componentwise Perturbation Analysis of the Schur Decomposition of a Matrix, Random Matrices Generating Large Growth in LU Factorization with Pivoting, Norm and Trace Estimation with Random Rank-one Vectors, Algebraic Error Analysis for Mixed-Precision Multigrid Solvers, Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space, Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems, A Low-Rank Matrix Equation Method for Solving PDE-Constrained Optimization Problems, Efficient implementation of the Hardy–Ramanujan–Rademacher formula, Improved rigorous perturbation bounds for the LU and QR factorizations, On the pivot structure for the weighing matrixW(12,11), An inverse‐free ADI algorithm for computing Lagrangian invariant subspaces, Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors, On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity, Linear algebra software for large-scale accelerated multicore computing, Low-Rank Approximation of a Matrix: Novel Insights, New Progress, and Extensions, Approximate Calculation of Sums II: Gaussian Type Quadrature, Block classical Gram–Schmidt-based block updating in low-rank matrix approximation, Strassen's Algorithm for Tensor Contraction, Data-Driven Polynomial Ridge Approximation Using Variable Projection, Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides, Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering, Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in FEM simulations, Unnamed Item, Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic, Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations, The Runge Example for Interpolation and Wilkinson's Examples for Rootfinding, The binomial transform of p-recursive sequences and the dilogarithm function, Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices, Direct Function Evaluation versus Lookup Tables: When to Use Which?, Fast Low-Rank Kernel Matrix Factorization Using Skeletonized Interpolation, Iterative Solution of Saddle-Point Systems from Radial Basis Function (RBF) Interpolation, Error Analysis of ZFP Compression for Floating-Point Data, Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems, On the Sensitivity of Singular and Ill-Conditioned Linear Systems, Krylov Method Revisited with an Application to the Localization of Eigenvalues, Accurate and efficient evaluation of Schur and Jack functions, A New Approach to Probabilistic Rounding Error Analysis, Subdivision-Based Nonlinear Multiscale Cloth Simulation, Simulating Low Precision Floating-Point Arithmetic, Bayesian Probabilistic Numerical Methods, Block Modified Gram--Schmidt Algorithms and Their Analysis, How do you compute the midpoint of an interval?, On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems, Generalized Tensor Eigenvalue Problems, Conditioning of Leverage Scores and Computation by QR Decomposition, An Active-Set Method for Second-Order Conic-Constrained Quadratic Programming, Analytic continuation of the3F2hypergeometric series, New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential, New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously, Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems, Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices, $\mathcal{H}_2$-Optimal Model Reduction Using Projected Nonlinear Least Squares, Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems, Stochastic Rounding and Its Probabilistic Backward Error Analysis, Generating Extreme-Scale Matrices With Specified Singular Values or Condition Number, An Algorithm for the Matrix Lambert $W$ Function, Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms, Numerical Optimization for the Length Problem, Relations between Transfer Matrices and Numerical Stability Analysis to Avoid the $\Omega d$ Problem, The Fast Implementation of Higher Order Hermite--Fejér Interpolation, Preconditioned Multishift BiCG for $\mathcal{H}_2$-Optimal Model Reduction, A Radix-Independent Error Analysis of the Cornea-Harrison-Tang Method, Algorithm 960, On BLAS Level-3 Implementations of Common Solvers for (Quasi-) Triangular Generalized Lyapunov Equations, Chaos Game Representation, Algorithm 1021: SPEX Left LU, Exactly Solving Sparse Linear Systems via a Sparse Left-looking Integer-preserving LU Factorization, The Joint Bidiagonalization Method for Large GSVD Computations in Finite Precision, Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores, Randomized Algorithms for Rounding in the Tensor-Train Format, Tensors in computations, Mixed precision algorithms in numerical linear algebra, Phase function methods for second order linear ordinary differential equations with turning points, Pharmacokinetic parameter identification using a meshless method approach for transdermal drug delivery, Calculating the divided differences of the exponential function by addition and removal of inputs, Floating-point arithmetic, Accurate computation of eigenvalues of generalized sign regular quasi-Said-Ball-Vandermonde matrices, Stochastic Rounding Variance and Probabilistic Bounds: A New Approach, The \(\mathbb{DL}(P)\) vector space of pencils for singular matrix polynomials, SCORE: approximating curvature information under self-concordant regularization, Convergence Analysis of a Mixed Precision Parareal Algorithm, Complete decomposition of symmetric tensors in linear time and polylogarithmic precision, Validated Root Enclosures for Interval Polynomials with Multiplicities, Fast evaluation and root finding for polynomials with floating-point coefficients, Numerical methods for parametric model reduction in the simulation of disk brake squeal, Generalized Matrix Nearness Problems, Universal MATLAB‐based square‐root solutions in the family of continuous‐discrete Gaussian filters for state estimation in nonlinear stochastic dynamic systems, Recursive solution of initial value problems with temporal discretization, Fast and accurate computation of the Euclidean norm of a vector, Discrete Lotka-Volterra with shift algorithm for computing matrix eigenvalues and singular values, Accuracy and stability of quaternion Gaussian elimination, On the accuracy of de Casteljau-type algorithms and Bernstein representations, Pebbling Game and Alternative Basis for High Performance Matrix Multiplication, Power and sample size for random coefficient regression models in randomized experiments with monotone missing data, Precision-aware deterministic and probabilistic error bounds for floating point summation, Nonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data, On computing the symplectic \(LL^T\) factorization, Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning, Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank, Householder Orthogonalization with a Nonstandard Inner Product, Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation, Langevin dynamics simulation with dipole-dipole interactions: massive performance improvements and advanced analytical integrator, Parameter choice strategies for error expressions and the numerical stability of Tikhonov-regularized approximation formulae, The lifetime of micron scale topological chiral magnetic states with atomic resolution, On the Deep Active-Subspace Method, The Jordan and Frobenius pairs of the inverse, A new multipoint symmetric secant method with a dense initial matrix, Tight computationally efficient approximation of matrix norms with applications, Condition numbers of the mixed least squares-total least squares problem revisited, Growth Factors of Random Butterfly Matrices and the Stability of Avoiding Pivoting, Probabilistic Rounding Error Analysis of Householder QR Factorization, Teaching linear algebra in a mechanized mathematical environment, Verified correctness, accuracy, and convergence of a stationary iterative linear solver: Jacobi method, Branch-and-bound performance estimation programming: a unified methodology for constructing optimal optimization methods, Limitations of neural network training due to numerical instability of backpropagation, Roundoff error analysis of the double-exponential formula-based method for the matrix sign function, The forward rounding error analysis of the partial pivoting quaternion LU decomposition, Estimates on the dimension of self‐similar measures with overlaps, The accurate and efficient solutions of linear systems for generalized sign regular matrices with certain signature, Rigorous computation of linear response for intermittent maps, A mixed precision LOBPCG algorithm, Pseudospectral shattering, the sign function, and diagonalization in nearly matrix multiplication time, Fast practical lattice reduction through iterated compression, High-order lifting for polynomial Sylvester matrices, Formally-verified round-off error analysis of Runge-Kutta methods, On stochastic roundoff errors in gradient descent with low-precision computation, Numerical stability and tensor nuclear norm, Five-Precision GMRES-Based Iterative Refinement, CCOMP: an efficient algorithm for complex roots computation of determinantal equations, Singular value decomposition in extended double precision arithmetic, A cost-efficient numerical algorithm for the determinants of heptadiagonal matrices with Toeplitz structure, An implicit spin lattice dynamics integrator in LAMMPS, Adaptively restarted block Krylov subspace methods with low-synchronization skeletons, Rounding error analysis of linear recurrences using generating series, The Joint Bidiagonalization of a Matrix Pair with Inaccurate Inner Iterations, Comparison of approximate and numerical methods for solving the homogeneous Dirichlet problem for the Helmholtz operator in a two-dimensional domain, Acceleration of iterative refinement for singular value decomposition, Accurate bidiagonal factorization of quantum Hilbert matrices, An immersed selective discontinuous Galerkin method in particle-in-cell simulation with adaptive Cartesian mesh and polynomial preserving recovery, Sharper Bounds for Proximal Gradient Algorithms with Errors, Adaptive Precision Sparse Matrix–Vector Product and Its Application to Krylov Solvers, Double precision is not necessary for LSQR for solving discrete linear ill-posed problems, On a special basis of approximate eigenvectors with local supports for an isolated narrow cluster of eigenvalues of a symmetric tridiagonal matrix, Parameter identification of a phase-field fracture model using integrated digital image correlation, Approximating Higher-Order Derivative Tensors Using Secant Updates, Numerical stability of algorithms at extreme scale and low precisions, On computing modified moments for half-range Hermite weights, Fast exact Bayesian inference for sparse signals in the normal sequence model, Unnamed Item, Unnamed Item, Symbolic-numeric sparse interpolation of multivariate polynomials, Verified error bounds for multiple roots of systems of nonlinear equations, Polynomial least squares fitting in the Bernstein basis, New rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix, Bidiagonal decomposition of rectangular totally positive Said-Ball-Vandermonde matrices: error analysis, perturbation theory and applications, A computational status update for exact rational mixed integer programming, A computational status update for exact rational mixed integer programming, Mixed and componentwise condition numbers for matrix decompositions, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization, Conditioning theory of the equality constrained quadratic programming and its applications, Perturbation analysis for the QX factorization for centrosymmetric matrices, Deflation for the Symmetric Arrowhead and Diagonal-Plus-Rank-One Eigenvalue Problems, Randomized Gram--Schmidt Process with Application to GMRES, Error analysis of the truncated Taylor series expansion method for computing matrix exponential, On condition numbers of quaternion matrix inverse and quaternion linear systems with multiple right-hand sides, A stochastic method for solving time-fractional differential equations, Exact QR factorizations of rectangular matrices
Uses Software
