Keywords: Structured Sylvester equation; Multiplicative perturbation; Generalized polar decomposition; Frobenius norm bound; Moore-Penrose inverse; 15A09; 15A23; 15A24; 15A60; 65F35;
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Keywords: 15A52; 15A45; 60H25; 65F35; Contracted product; Matricization; Tensor; Norm inequality; Commutator;
Keywords: 15A09; 15A12; 65F35; Linear least squares problem with equality constraints; Linear least squares; Componentwise perturbation; Condition number; Hager-Higham algorithm;
Keywords: 15A60; 47A12; 65F35; Field of values; Numerical radius; Singular subspaces; Crouzeix's conjecture;
Keywords: 65F35; 15A23; 15A57; LU factorization; Cholesky factorization; QR factorization; Structured condition number; Structured matrix;
Keywords: 65F35; 47G10; 74B99; Condition number; Error analysis; Integral operator; Peridynamics; Nonlocal diffusion; Preconditioning;
Keywords: 15A18; 65F35; Matrix polynomial; Eigenvalue; Perturbation; Singular value; Jordan chain;
Keywords: 15A54; 15A60; 15B05; 65F15; 65F35; 93B18; Backward error analysis; Dual minimal bases; Genericity; Linearizations; â-Ifications; Minimal bases; Minimal indices; Perturbations; Polynomial matrices; Robustness; Sylvester matrices;
Keywords: 15B48; 42C15; 65F35; Scalable frames; Condition number; Tight frame;
Keywords: 65F05; 65F15; 65F35; Sign regular matrices; Almost strictly sign regular matrices; Backward stability; Backward error;
Keywords: primary; 65F10; secondary; 65F08; 65F35; Singular nonsymmetric saddle point problem; Iterative methods; Manteuffel algorithm; Optimal parameters; Optimal semi-convergence factor;
Keywords: 15A06; 15A52; 15A12; 65F05; 65F35; Gaussian elimination; Pivoting; Block Gaussian elimination; Preconditioning; Random matrix algorithms; Linear systems of equations;
Keywords: 65F10; 65F30; 65F35; 65F15; Limited-memory quasi-Newton methods; Compact representation; Broyden class of updates; Symmetric rank-one update; Broyden-Fletcher-Goldfarb-Shanno update; Davidon-Fletcher-Powell update; Sherman-Morrison-Woodbury
Keywords: 65F35; 15A69; 15A72; 65H04; 14Q15; 14N05; 58A05; 58A07; Tensor rank decomposition; CP; Condition number; Stability analysis; Terracini's matrix;
Keywords: 15A18; 65F35; 65F15Matrix; Eigenvalue; Perturbation; Singular value
Keywords: 15A12; 15A18; 15A22; 65F15; 65F35; 65F50Statistical condition estimation; Generalized eigenvalue problem; Deflating subspace; Large-scale problem; Sylvester equation; Newton’s method
Keywords: Generalized inverse; Restricted linear system; Convergence analysis; Cramer rule; Subproper splitting; Characterization15A09; 65F05; 65F15; 65F35
Keywords: 15A60; 15A45; 15A27; 65F35; 65F30; Commutator; Joint diagonalizability; Pseudo-metric;
Keywords: 65F05; 65F35; 15A06; 15A52; 15A12Randomized matrix algorithms; Gaussian random matrices; Singular subspaces of a matrix; Duality; Derandomization; Sparse and structured preprocessors
Schatten properties, nuclearity and minimality of phase shift invariant spaces
Keywords: primary; 47Bxx; 45P05; 35S05; 42B35; secondary; 65F35; 46A16; 42C15; Matrices; Modulation spaces; Non-uniform expansions; Minimality; Singular values; Nuclear operators;
The convergence theory for the restricted version of the overlapping Schur complement preconditioner
Keywords: Restricted version of overlapping Schur complement; Convergence theory; Restricted additive Schwarz methods; Nonnegative matrix; 65F10; 65F35; 65M55;
Structured distance to normality of tridiagonal matrices
Keywords: 65F15; 65F35; 15B05; 15B57; Distance; Structured distance; Frobenius norm; Normal matrix; r-Toeplitz matrix; Tridiagonal matrix;
Signal flow graph approach to efficient and forward stable DST algorithms
Keywords: 15A23; 15B10; 65F35; 65F50; 65T50; 65Y04; 65Y05; 65Y20; 94A12; Discrete sine transform; Efficient and recursive algorithms; Arithmetic complexity; Error bound and stability; Sparse and orthogonal matrices; Signal flow graphs;
Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem
Keywords: 15A09; 15A12; 65F35; Total least squares problem; Componentwise perturbation; Condition number; Adjoint operator; Structured perturbation;
QR decomposition of almost strictly sign regular matrices
Keywords: 65F05; 65F15; 65F35; Sign regular matrices; Almost strictly sign regular matrices; LDU factorization; QR factorization;
Structured condition numbers and small sample condition estimation of symmetric algebraic Riccati equations
Keywords: Symmetric algebraic Riccati equation; Perturbation analysis; Condition number; Statistical condition estimation; 15A09; 15A12; 65F35;
The inverse q-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix
Keywords: 15A18; 15A29; 15A60; 65F15; 65F35; Eigenvalues; Ritz values; Numerical range; Field of values; Davis-Wielandt shell; Inverse numerical range problem;
Almost strictly sign regular matrices and Neville elimination with two-determinant pivoting
Keywords: Almost strictly sign regular matrices; Neville elimination; Two-determinant pivoting65F05; 65F15; 65F35
A flexible condition number for weighted linear least squares problem and its statistical estimation
Keywords: 65F35; 15A12; 15A60Weighted norm; Condition number; Fréchet derivative; Weighted singular value decomposition; PCE method; SCE method
Rank-revealing decomposition of symmetric indefinite matrices via block anti-triangular factorization
Keywords: 65F30; 65F35; 15A23Indefinite symmetric matrix; Rank revealing; Inertia
On the conditioning of factors in the SR decomposition
Keywords: 65F25; 65F35; 65F05SR decomposition; Symplectic matrices; Skew-symmetric bilinear forms; Orthogonalization; Condition number
Perturbation analysis for the matrix least squares problem AXB=CAXB=C
Keywords: 65F20; 65F35; 15A09Matrix equation; Least squares solution; Perturbation bound; Norm-preserving dilation
On positive definite solutions of the nonlinear matrix equations X±A*XqA=QX±A*XqA=Q
Keywords: Nonlinear matrix equations; Positive definite solution; Iterative methods15A24; 65H05; 65F35
Estimating the norms of random circulant and Toeplitz matrices and their inverses
Keywords: 15A12; 15A52; 65F22; 65F35; Matrix norms; Condition numbers; Toeplitz matrices; Circulant matrices; Random matrices;
Condition numbers for the nonlinear matrix equation and their statistical estimation
Keywords: 65F35; 15A12; 15A60Nonlinear matrix equation; Normwise condition number; Mixed and componentwise condition numbers; Probabilistic spectral norm estimator; SCE method
A CS decomposition for orthogonal matrices with application to eigenvalue computation
Keywords: 65F15; 15A23; 15A18; 15B10; 65G50; 65F35; Orthogonal matrix; Eigenvalue problem; Full CS decomposition; High accuracy;
Triangular truncation of k-Fibonacci and k-Lucas circulant matrices
Keywords: primary; 15B36; secondary; 65F35; Triangular truncation; Fibonacci numbers; Spectral norm;
A fast recursive orthogonalization scheme for the Macaulay matrix
Keywords: 65F25; 65F35; 65F50; 15A18Macaulay matrix; Orthogonal bases; Multivariate polynomials; Recursive orthogonalization
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Keywords: 65F10; 65F50; 65F08; 65F22; 65F35; Block two-by-two linear system; Generalized parameterized inexact Uzawa method; Preconditioning; Krylov subspace method; Convergence;
New bounds for roots of polynomials based on Fiedler companion matrices
Keywords: 15A18; 15A60; 15B99; 65F15; 65F35; 65H04; Bounds; Eigenvalues; Fiedler companion matrices; Matrix norms; Roots of polynomials;
Conditioning and accurate computations with Pascal matrices
Keywords: 65F05; 65F15; 65F35; Pascal matrices; Bidiagonal factorizations; Accurate computations; Conditioning; Vandermonde matrices;
Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation
Keywords: 65F10; 65F35; Parameterized preconditioning; Generalized saddle point problem; Stokes equation; Spectral condition number; Eigenvalue estimate;
Stable solutions of linear systems involving long chain of matrix multiplications
Keywords: 15A09; 15A12; 65F05; 65F35; 82B80Graded QR decomposition; Singular value decomposition; Condition number; Numerical stability; Quantum Monte Carlo
On the implementation of 3D Galerkin boundary integral equations
Keywords: Galerkin approximation; Sparse preconditioner; Singular integrals; Hypersingular integrals; Boundary element method; Triangular boundary; Potential theory; Incomplete LU; Iterative methods35J25; 65N38; 65R20; 65F10; 65F35; 65F50
On positive definite solutions of nonlinear matrix equation Xs-AâX-tA=Q
Keywords: 15A24; 65F15; 65F35; Nonlinear matrix equation; Positive definite solution; Iteration; Perturbation estimates; Fixed-point theorem;
Eigenvalue bounds for the Schur complement with a pressure convection–diffusion preconditioner in incompressible flow computations
Keywords: 65F10; 65F35; 65F22; 65N25Non-symmetric saddle point problems; Preconditioning; Schur complement; Finite element methods; Navier–Stokes equations
Finite element wavelets with improved quantitative properties
Keywords: 65T60; 65N30; 65F35; 65R20Finite element; Wavelet; Riesz basis; Cancellation property; Partial differential equation; Boundary integral equation
Eigenvalue estimates for a preconditioned Galerkin matrix arising from mixed finite element discretizations of viscous incompressible flows
Keywords: 65F10; 65F35; 65N22; 65N25; Nonsymmetric systems; Indefinite systems; Preconditioning; Finite element methods; Navier-Stokes equations;
A more accurate algorithm for computing the Christoffel transformation
Keywords: 65G50; 65F30; 65F35; 42C05Christoffel transformation; Forward stability; Roundoff error analysis; LR algorithm
How big can the commutator of two matrices be and how big is it typically?
Keywords: Primary 15A52; Secondary 15A45; 60H25; 65F35; Commutator; Random matrix; Frobenius norm;