Componentwise enclosure for solutions of least squares problems and underdetermined systems

DOI10.1016/j.laa.2013.11.044zbMath1329.65081OpenAlexW1996950783WikidataQ112882234 ScholiaQ112882234MaRDI QIDQ2442244

Shinya Miyajima

Publication date: 2 April 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.11.044

zbMATH Keywords

least squares problemsnumerical enclosureverified error boundunderdetermined systemsminimal 2-norm solutioncomponentwise estimation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Roundoff error (65G50) Algorithms with automatic result verification (65G20) Linear equations (linear algebraic aspects) (15A06)

Related Items (3)

Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C ⋮ A family of iterative methods with accelerated convergence for restricted linear system of equations ⋮ Accurate solutions of weighted least squares problems associated with rank-structured matrices

Uses Software

• INTLAB
• SparseMatrix
• mctoolbox
• VERSOFT

Cites Work

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• Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
• Fast enclosure for solutions in underdetermined systems
• Generalized inverses. Theory and applications.
• Verified Bounds for Least Squares Problems and Underdetermined Linear Systems
• The university of Florida sparse matrix collection
• Error bounds for approximate solutions of systems of equations
• Numerical Optimization
• Accuracy and Stability of Numerical Algorithms

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