scientific article; zbMATH DE number 852536
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Publication:4868585
zbMath0847.65023MaRDI QIDQ4868585
Publication date: 6 March 1996
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monographmethod of least squaresbibliographyCholesky factorizationiterative methodsGaussian eliminationconjugate gradient methodsQR decompositiondirect methodscondition numbersill-conditioned problemssingular value decompositionsiterative refinementsparse problemsmethod of normal equations
Linear regression; mixed models (62J05) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical solutions to equations with linear operators (65J10) Probabilistic methods, stochastic differential equations (65C99)
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II: The discrete least-squares problem, An efficient Gauss-Newton algorithm for solving regularized total least squares problems, A multilevel block incomplete Cholesky preconditioner for solving normal equations in linear least squares problems, Learning to Forecast Dynamical Systems from Streaming Data, Nonintrusive Reduced-Order Models for Parametric Partial Differential Equations via Data-Driven Operator Inference, The Joint Bidiagonalization of a Matrix Pair with Inaccurate Inner Iterations, Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics, Double precision is not necessary for LSQR for solving discrete linear ill-posed problems, A regularized interior-point method for constrained linear least squares, The Joint Bidiagonalization Method for Large GSVD Computations in Finite Precision, Mixed precision algorithms in numerical linear algebra, Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement, A Generalized Dual Transform: Linear Algebra and Geometry of (Pseudo)Inverting a Matrix, Geometric Versus Arithmetic Difference and $$H^1$$ -Seminorm Versus $$L^2$$ -Norm in Function Approximation, A Hybrid Gibbs Sampler for Edge-Preserving Tomographic Reconstruction with Uncertain View Angles, Parameter choices for sparse regularization with the ℓ1 norm *, Stable Computation of Least Squares Problems of the OGM(1,N) Model and Short-Term Traffic Flow Prediction, A Computational Study of Using Black-box QR Solvers for Large-scale Sparse-dense Linear Least Squares Problems, Greedy Tikhonov regularization for large linear ill-posed problems, Direct Implementation of Tikhonov Regularization for the First Kind Integral Equation, Least squares orthogonal polynomial regression estimation for irregular design, Scaling Up Parallel Computation of Tiled QR Factorizations by a Distributed Scheduling Runtime System and Analytical Modeling, An Iterative Reduction FISTA Algorithm for Large-Scale LASSO, Linear optimization over homogeneous matrix cones, Numerical convergence and error analysis for the truncated iterative generalized stochastic perturbation-based Finite element method, Quasi-periodic waves and asymptotic behavior for a coupled nonlinear Klein-Gordon equation, An efficient implementation of the Gauss-Newton method via generalized Krylov subspaces, On Using Cholesky-Based Factorizations and Regularization for Solving Rank-Deficient Sparse Linear Least-Squares Problems, Generalized Matrix Nearness Problems, Identification of the thermal conductivity tensor for transversely isotropic materials, Combined invariant subspace \& frequency-domain subspace method for identification of discrete-time MIMO linear systems, A computational framework for edge-preserving regularization in dynamic inverse problems, Pandemic management by a spatio-temporal mathematical model, M-IHS: an accelerated randomized preconditioning method avoiding costly matrix decompositions, One Study of COVID-19 Spreading at The United States - Brazil - Colombia, Two-parameter block triangular splitting preconditioner for block two-by-two linear systems, Accelerated greedy randomized augmented Kaczmarz algorithm for inconsistent linear systems, Hermite least squares optimization: a modification of BOBYQA for optimization with limited derivative information, Convergence properties of Levenberg-Marquardt methods with generalized regularization terms, A mass transfer cavitation model for the numerical flow simulation of binary alkane mixture segregation, Time discretization in the solution of parabolic PDEs with ANNs, Householder Orthogonalization with a Nonstandard Inner Product, A method for computing inverse parametric PDE problems with random-weight neural networks, Fast convergence strategy for ambiguous inverse problems based on hierarchical regularization, Simultaneous Identification and Denoising of Dynamical Systems, Condition numbers of the mixed least squares-total least squares problem revisited, Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations, An extreme learning machine-based method for computational PDEs in higher dimensions, A Gauss-Newton method for mixed least squares-total least squares problems, Tracking hematopoietic stem cell evolution in a Wiskott-Aldrich clinical trial, On greedy randomized block Gauss-Seidel method with averaging for sparse linear least-squares problems, Preconditioners for Krylov subspace methods: An overview, Fast Computation of Spectral Projectors of Banded Matrices, An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation, Mathematical model for BCG-based treatment of type 1 diabetes, Horseshoe Priors for Edge-Preserving Linear Bayesian Inversion, Computation of conditional expectations with guarantees, Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES, Error bounds for a least squares meshless finite difference method on closed manifolds, Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations, EXTENDING THE APPLICABILITY OF INEXACT GAUSS-NEWTON METHOD FOR SOLVING UNDERDETERMINED NONLINEAR LEAST SQUARES PROBLEMS, A New GSOR Method for Generalised Saddle Point Problems, An iterative algorithm to solve the generalized Sylvester tensor equations, Simplifying numerical solution of constrained PDE systems through involutive completion, On Iterative Solution of the Extended Normal Equations, Fast computation of zeros of polynomial systems with bounded degree under finite-precision, CG Variants for General-Form Regularization with an Application to Low-Field MRI, An Efficient Semi-Analytical Method to Compute Displacements and Stresses in an Elastic Half-Space with a Hemispherical Pit, Approximation of High-Dimensional Periodic Functions with Fourier-Based Methods, A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations, Iteratively Reweighted FGMRES and FLSQR for Sparse Reconstruction, Fast Nonnegative Least Squares Through Flexible Krylov Subspaces, Solving large nonlinear generalized eigenvalue problems from density functional theory calculations in parallel, Border estimation of a two-dimensional uniform distribution if data are measured with additive error, Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems, Data-Driven Polynomial Ridge Approximation Using Variable Projection, Numerical solutions of symmetric saddle point problem by direct methods, Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares, Rectangular Vandermonde matrices on Chebyshev nodes, Least squares scattered data fitting by truncated SVDs, Physical Modeling of Turbocharged Engines and Parameter Identification, Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm, Polynomial least squares fitting in the Bernstein basis, Bidiagonal decomposition of rectangular totally positive Said-Ball-Vandermonde matrices: error analysis, perturbation theory and applications, Applications of convex separable unconstrained nonsmooth optimization to numerical approximation with respect to l1- and l∞-norms, An Efficient Proximal Block Coordinate Homotopy Method for Large-Scale Sparse Least Squares Problems, Nonconvex Lagrangian-Based Optimization: Monitoring Schemes and Global Convergence, Unnamed Item, A numerical study on Neumann-Neumann methods forhpapproximations on geometrically refined boundary layer meshes II. Three-dimensional problems, Response functions in linear viscoelastic constitutive equations and related fractional operators, Sparse Stretching for Solving Sparse-Dense Linear Least-Squares Problems, On the Sensitivity of Singular and Ill-Conditioned Linear Systems, A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy, Flexible Krylov Methods for $\ell_p$ Regularization, Spectral Computed Tomography with Linearization and Preconditioning, Block Modified Gram--Schmidt Algorithms and Their Analysis, Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems, Restrictively Preconditioned Conjugate Gradient Method for a Series of Constantly Augmented Least Squares Problems, Convergence Analysis of Inexact Randomized Iterative Methods, Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems, Parallel Computation of Entries of ${A}^{-1}$, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, Condition numbers for the K-weighted pseudoinverse and their statistical estimation, KRYLOV SUBSPACE METHODS WITH DEFLATION AND BALANCING PRECONDITIONERS FOR LEAST SQUARES PROBLEMS, Total least squares problems on infinite dimensional spaces, A fast method for simultaneous reconstruction and segmentation in X-ray CT application, Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation, Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation
