Keywords: Partitioned matrix; Gauss-Jordan elimination; Weighted Moore-Penrose inverse; Computational complexity; 15A09; 65F05;
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Keywords: Distortion; Encoding/decoding maps; Dilatation; Extension; Upper-triangular kinematics; 15A06; 65F05; 74A05; 74A10; 74A15; 74A20;
Keywords: 65F05; 65F15; 65F35; Sign regular matrices; Almost strictly sign regular matrices; Backward stability; Backward error;
Keywords: 65F05; 65F15; 65D05; 15A23; 15B05; 15B48; Cauchy-Vandermonde matrix; Totally positive matrix; Neville elimination; Bidiagonal decomposition; High relative accuracy;
Keywords: 41A20; 60J22; 65F05; Cyclic reduction; Quasiseparable matrices; Rational interpolation; Sylvester equations; Exponential decay; Block tridiagonal systems;
Keywords: 15A06; 15A52; 15A12; 65F05; 65F35; Gaussian elimination; Pivoting; Block Gaussian elimination; Preconditioning; Random matrix algorithms; Linear systems of equations;
Keywords: Binet formula; Generalized Fibonacci sequences; Vandermonde systems; Special generalized Vandermonde systems11B99; 15B99; 65F05; 97N50
Keywords: 15A06; 15A45; 65F05; 65G30Symmetric solution set; Persymmetric solution set; Skew-symmetric solution set; Perskew-symmetric solution set; Beeck criterion; Hartfiel inequalities; Oettli–Prager inequality; Interval analysis
Keywords: 65F05; 65F15; 65F35Almost strictly sign regular matrices; Neville elimination; Characterization
Keywords: 15A09; 15A15; 15A23; 15A33; 65F05; Computational complexity; Determinant; Inverse matrix; Pentadiagonal matrix; Structured matrix;
Keywords: 65F05; 15A48; 65F40Sign regular matrices; Almost strictly totally negative matrices; Neville elimination
Keywords: Generalized inverse; Restricted linear system; Convergence analysis; Cramer rule; Subproper splitting; Characterization15A09; 65F05; 65F15; 65F35
Keywords: 65F05; 65F30; 65G20; 65G50Saddle point linear systems; Error estimation; Verified error bound
Keywords: 65F05; 15A06; 15A12; Symmetric indefinite matrices; Matrix factorization; Bunch-Kaufman; Bunch-Parlett;
Keywords: 65F05; 65F10; 65F15; 65F50; 65T50Nonnegative matrices; Eventually nonnegative matrices; Power nonnegative matrices; Stochastic matrices; Perron–Frobenius theory
Keywords: 65F05; 65F30; 65G20; 65G50Matrix function; Matrix inverse square root; Numerical enclosure; Verified computation
Keywords: 15A04; 15A06; 15A09; 47A65; 65D05; 65F05; 68Q25Transformations of matrix structures; Vandermonde matrices; Cauchy matrices; Multipole method; HSS matrices; Toeplitz matrices
Keywords: 65F05; 15A23Inertia; Symmetric factorization
Keywords: 65F05; 46L05; 11Y50Asymptotically nonexpansive random mappings; Implicit iterative process; Weak and strong convergence; Common random fixed points; Condition (B); Opial’s condition
Keywords: 65F05; 65G20Matrix inverse square root; Matrix sign function; Interval arithmetic; Krawczyk's method; Verified computation
Keywords: 15A09; 15A18; 15A23; 65F05; 65F08; 65F10; 65F15; Block two-by-two matrix; Nonsingularity; Rank; Singular value decomposition; Moore-Penrose pseudoinverse;
Keywords: 65F05; 65F35; 15A06; 15A52; 15A12Randomized matrix algorithms; Gaussian random matrices; Singular subspaces of a matrix; Duality; Derandomization; Sparse and structured preprocessors
Inversion and pseudoinversion of block arrowhead matrices
Keywords: Block arrowhead matrix; Matrix inverse; Moore-Penrose inverse; Symbolic computation; Schur complement; 15A09; 65F05;
On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
Keywords: 35J05; 65F05; 65F50; 65N30; 65Y05; Fast direct solver; GPU computing; Partial solution technique; PSCR method; Roofline model; Separable block tridiagonal linear system;
An efficient LDU algorithm for the minimal least squares solution of linear systems
Keywords: 65F05; 65F20; 1504; 6504; Minimum linear least squares; LDU; Null subspaces;
Threshold incomplete factorization constraint preconditioners for saddle-point matrices
Keywords: 15A23; 65F05; 65F50; Saddle-point matrices; Transformation; Incomplete factorization; Constraint preconditioner;
QR decomposition of almost strictly sign regular matrices
Keywords: 65F05; 65F15; 65F35; Sign regular matrices; Almost strictly sign regular matrices; LDU factorization; QR factorization;
Characterization of AE solution sets of parametric linear systems based on the techniques of convex sets
Keywords: 65F05; 65G99; 52B12; Linear parametric system; AE solution set; Convex set; Polytope; Minkowski sum; Support function;
Gauss-Jordan elimination method for computing all types of generalized inverses related to the {1}-inverse
Keywords: 15A09; 65F05; Generalized inverse; Moore-Penrose inverse; Gauss-Jordan elimination; Computational complexity;
Approximate least common multiple of several polynomials using the ERES division algorithm
Keywords: 15A23; 65F05; 65F30; 65Y20; Greatest common divisor; Linear systems; Shifting operation; Numerical errors; Least squares;
Matrix decomposition algorithms for arbitrary order C0C0 tensor product finite element systems
Keywords: 65F05; 65N22; 65N30Poisson’s equation; Finite element Galerkin method; C0C0 piecewise polynomials; Matrix decomposition algorithms
Random multipliers numerically stabilize Gaussian and block Gaussian elimination: Proofs and an extension to low-rank approximation
Keywords: 15A52; 15A12; 15A06; 65F22; 65F05; Random matrices; Random multipliers; Gaussian elimination; Pivoting; Block Gaussian elimination; Low-rank approximation; SRFT matrices; Random circulant matrices;
Componentwise error analysis for linear systems associated with sign regular matrices
Keywords: 65F05; 65G50; 15A23; Sign regular matrices; Gaussian elimination; Componentwise error analysis;
Componentwise backward error analysis of Neville elimination
Keywords: 65G50; 15A23; 65F05; Neville elimination; Componentwise error analysis; Sign regular matrices; Pivoting;
Optimal rank matrix algebras preconditioners
Keywords: 65F05; 65F10; 65F15; 65F50; 65T50; Preconditioning; Matrix algebras; Toeplitz; Hankel; Clustering; Fast discrete transforms;
Conditioning and accurate computations with Pascal matrices
Keywords: 65F05; 65F15; 65F35; Pascal matrices; Bidiagonal factorizations; Accurate computations; Conditioning; Vandermonde matrices;
On new algorithms for inverting Hessenberg matrices
Keywords: 15A09; 15A15; 15A23; 65F05; 65Y20; Computational complexity; Hessenberg matrix; Inverse matrix; Matrix factorization;
Non-symbolic algorithms for the inversion of tridiagonal matrices
Keywords: 15A09; 15A15; 15A29; 39A06; 65F05; 65Y20; Computational complexity; Difference equation; Inverse matrix; Numerical algorithm; Tridiagonal matrix;
Componentwise error analysis for the block LU factorization of totally nonnegative matrices
Keywords: 15A23; 65F05; Block LU factorization; Totally nonnegative matrices; Componentwise error analysis;
Accurate solution of dense linear systems, Part II: Algorithms using directed rounding
Keywords: 65F05; 65G20Linear systems; Matlab; Data with tolerances; Inner bounds; (Extremely) ill-conditioned matrices; Rigorous error bounds
A note on matrices with maximal growth factor for Neville elimination
Keywords: 65F05; 65G05Neville elimination; Growth factor; Row pivoting strategies
Efficient numerical solution of the generalized Dirichlet–Neumann map for linear elliptic PDEs in regular polygon domains
Keywords: 15A06; 15A90; 15A57; 65F05; 65F10; 65N35; 15A57; 35J25Elliptic PDEs; Dirichlet–Neumann map; Global Relation; Collocation; Block circulant matrices; Fast Fourier Transform (FFT)
Growth factors of pivoting strategies associated with Neville elimination
Keywords: 65F05; 65G05Neville elimination; Pivoting; Growth factor; Total positivity
A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations
Keywords: 65N35; 76M20; 65F05; 35J05; 76D30ADI; Direction splitting; Incompressible flows; Navier–Stokes; Pressure Poisson equation; Time splitting
High-resolution boosted deconvolution of spectroscopic data
Keywords: 65F05; 65F10; 65F22; 65Z05Positive definite deconvolution algorithms; Boosted deconvolution; Decomposition to δδ-functions; Resolution improvement; Decomposition of clusters of peaks; Multidimensional γγ-ray spectra
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
How ordinary elimination became Gaussian elimination
Keywords: 01-08; 62J05; 65-03; 65F05; 97-03Algebra before 1800; Gaussian elimination; Human computers; Least squares method; Mathematics education
A direct method to solve block banded block Toeplitz systems with non-banded Toeplitz blocks
Keywords: 65F05; 15A57Toeplitz matrices; Block Toeplitz Toeplitz block matrices; Sherman–Morrison–Woodbury formula; Fast Toeplitz solver
Saving flops in LU based shift-and-invert strategy
Keywords: 15A18; 15A23; 34L16; 65F05; 65F15Shift-and-invert; Eigenvalue; Divide and conquer; LU factorization
A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems
Keywords: 65F05; 65Y05; 68M14Toeplitz; Pentadiagonal; Linear systems; Fast algorithm; Perturbation analysis; Natural quintic splines