Moments of a linear operator, with applications to the trace of the inverse of matrices and the solution of equations

DOI10.1002/nla.803zbMath1289.15014OpenAlexW2139873872MaRDI QIDQ2864484

Paraskevi Fika, Marilena Mitrouli, Claude Brezinski

Publication date: 6 December 2013

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.803

zbMATH Keywords

numerical resultssingular value decompositiontraceinterpolation conditionsextrapolation of the moments

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Linear equations (linear algebraic aspects) (15A06)

Related Items (13)

Estimation of the bilinear form \(y^\ast f(A)x\) for Hermitian matrices ⋮ New matrix function approximations and quadrature rules based on the Arnoldi process ⋮ Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse ⋮ GCV for Tikhonov regularization by partial SVD ⋮ Estimating the trace of matrix functions with application to complex networks ⋮ The extended global Lanczos method, Gauss-Radau quadrature, and matrix function approximation ⋮ Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides ⋮ Vector estimates for \(f(A)\mathbf b\) via extrapolation ⋮ Simplified anti-Gauss quadrature rules with applications in linear algebra ⋮ Stochastic estimates for the trace of functions of matrices via Hadamard matrices ⋮ GCV for Tikhonov regularization via global Golub–Kahan decomposition ⋮ Unnamed Item ⋮ Bounding matrix functionals via partial global block Lanczos decomposition

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