Verified Bounds for Least Squares Problems and Underdetermined Linear Systems

DOI10.1137/110840248zbMath1255.65082OpenAlexW2158149279MaRDI QIDQ2903115

Siegfried Michael Rump

Publication date: 23 August 2012

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/dc512bc26f9e67b0d41c59ff32d8f7fae1ccd516

zbMATH Keywords

algorithmnumerical experimentsnormal equationslinear least squares problemunderdetermined linear systemverified error boundssparse problemextra-precise residual evaluation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Algorithms with automatic result verification (65G20)

Related Items (8)

Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C ⋮ Verification of a low-degree polynomial vanishing at empirical points ⋮ Componentwise enclosure for solutions of least squares problems and underdetermined systems ⋮ A sharp error bound of the approximate solutions for saddle point linear systems ⋮ A heuristic verification of the degree of the approximate GCD of two univariate polynomials ⋮ The verification of multiplicity support of a defective eigenvalue of a real matrix ⋮ Improved componentwise verified error bounds for least squares problems and underdetermined linear systems ⋮ Convergence of Rump’s method for computing the Moore-Penrose inverse

Uses Software

• Matlab
• INTLAB
• SparseMatrix
• XBLAS

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