Methods for obtaining reliable solutions to systems of linear algebraic equations

DOI10.1007/s10559-011-9290-xzbMath1302.65082OpenAlexW2079263798MaRDI QIDQ464846

Ivan V. Sergienko, M. F. Yakovlev, A. N. Khimich

Publication date: 30 October 2014

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-011-9290-x

zbMATH Keywords

algorithmregularizationiterative methodssymmetric positive semidefinite matricesapproximate initial dataincompatible systemssystems of linear algebraic equationstotal error of the solution

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10)

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Piecewise polynomial algorithms for the analysis of processes in inhomogeneous media ⋮ Adaptive computer technologies for solving problems of computational and applied mathematics ⋮ Computer simulation system for nonlinear processes described by the Korteweg-de Vries-Burgers equation ⋮ Analysis of generalized Glushkov integral models with controllable memory based on the V. K. Dzyadyk \(a\)-method ⋮ Inverse diffraction problem of determining the properties of a plasma object ⋮ A meshless method of solving three-dimensional nonstationary heat conduction problems in anisotropic materials ⋮ Multidimensional scaling by means of pseudoinverse operations

Cites Work

• Analytical representation of perturbations of pseudoinverse matrices
• Perturbation bounds for the least squares problem
• The total error in calculating linear mathematical models by iterative methods
• Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems
• An Estimate for the Condition Number of a Matrix
• Expansions and polynomial limit representations of weighted pseudoinverses
• Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products
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