Randomized preprocessing of homogeneous linear systems of equations
From MaRDI portal
Publication:968998
DOI10.1016/j.laa.2010.01.023zbMath1202.65038OpenAlexW2017951318MaRDI QIDQ968998
Publication date: 11 May 2010
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2010.01.023
conditioningnumerical stabilitymatrix productsgeneralized inversesmatrix inversioncondition numberssystems of linear equationsNewton's iterationrandomized preprocessing
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Preconditioners for iterative methods (65F08)
Related Items
Numerically safe Gaussian elimination with no pivoting, Effective matrix-free preconditioning for the augmented immersed interface method, Additive preconditioning for matrix computations, New studies of randomized augmentation and additive preprocessing, A Derivative-Free Nonlinear Least Squares Solver, Matrix computations and polynomial root-finding with preprocessing, Randomized preprocessing versus pivoting, Solving linear systems of equations with randomization, augmentation and aggregation, Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization, Root-finding by expansion with independent constraints, New progress in real and complex polynomial root-finding, Random multipliers numerically stabilize Gaussian and block Gaussian elimination: proofs and an extension to low-rank approximation
Uses Software
Cites Work
- The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
- Iterative inversion of structured matrices
- Additive preconditioning for matrix computations
- Matrix multiplication via arithmetic progressions
- Degeneration of structured integer matrices modulo an integer
- Additive preconditioning, eigenspaces, and the inverse iteration
- A new error-free floating-point summation algorithm
- Lower bounds for the condition number of Vandermonde matrices
- A stabilized superfast solver for indefinite Hankel systems
- Asymptotically fast solution of Toeplitz and related systems of linear equations
- Methods of aggregation
- On practical algorithms for accelerated matrix multiplication
- Parallel solution of Toeplitzlike linear systems
- A probabilistic remark on algebraic program testing
- On a new class of structured matrices
- Numerics of Gram-Schmidt orthogonalization
- How bad are Hankel matrices?
- Structured matrices and Newton's iteration: unified approach
- Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
- Design, analysis, and implementation of a multiprecision polynomial rootfinder
- Symbolic and numeric methods for exploiting structure in constructing resultant matrices
- Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations
- Stability analysis of the method of seminormal equations for linear least squares problems
- Smoothed analysis of \(\kappa(A)\)
- Randomized preprocessing versus pivoting
- Multivariate polynomials, duality, and structured matrices
- Generalized inverses of certain Toeplitz matrices
- Computations with quasiseparable polynomials and matrices
- Schur aggregation for linear systems and determinants
- Effect of small rank modification on the condition number of a matrix
- Tensor properties of multilevel Toeplitz and related matrices
- A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Estimating Extremal Eigenvalues and Condition Numbers of Matrices
- An Improved Newton Iteration for the Generalized Inverse of a Matrix, with Applications
- Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices
- On Computations with Dense Structured Matrices
- Additive Preconditioning for Matrix Computations
- A Superfast Algorithm for Toeplitz Systems of Linear Equations
- Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest
- How Can We Speed Up Matrix Multiplication?
- The Probability That a Numerical Analysis Problem is Difficult
- Eigenvalues and Condition Numbers of Random Matrices
- Generalized Nested Dissection
- Fast Probabilistic Algorithms for Verification of Polynomial Identities
- Decreasing the Displacement Rank of a Matrix
- Numerical Linear Algebra for High-Performance Computers
- Fast and Efficient Parallel Solution of Sparse Linear Systems
- Stable and Efficient Algorithms for Structured Systems of Linear Equations
- Accurate and Efficient Floating Point Summation
- Accuracy and Stability of Numerical Algorithms
- Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure
- Accurate Floating-Point Summation Part I: Faithful Rounding
- Fast Solution of Toeplitz‐ and Cauchy‐Like Least‐Squares Problems
- Design, implementation and testing of extended and mixed precision BLAS
- Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
- Some Modified Matrix Eigenvalue Problems
- A unifying convergence analysis of second-order methods for secular equations
- Accurate Sum and Dot Product
- A bibliography on semiseparable matrices
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