A Theory of Condition

Previous article Next article A Theory of ConditionJohn R. RiceJohn R. Ricehttps://doi.org/10.1137/0703023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. L. Ashenhurst, Function evaluation in unnormalized arithmetic, J. Assoc. Comput. Mach., 11 (1964), 168–187 MR0163451 0123.33705 CrossrefISIGoogle Scholar[2] È. G. Belaga, Some problems involved in the calculation of polynomials, Dokl. Akad. Nauk SSSR, 123 (1958), 775–777 MR0105192 0099.33001 Google Scholar[3] George E. Forsythe and , Theodore S. Motzkin, An extension of Gauss' transformation for improving the condition of systems of linear equations, Math. Tables and Other Aids to Computation, 6 (1952), 9–17 MR0048162 0047.36203 CrossrefGoogle Scholar[4] M. Goldstein, Significance arithmetic on a digital computer, Comm. 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Mackensie, Introduction to Differentiable Manifolds, McGraw-Hill, New York, 1960 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Sensitivity of low-rank matrix recovery20 October 2022 | Numerische Mathematik, Vol. 152, No. 4 Cross Ref On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation27 September 2021 | Communications on Applied Mathematics and Computation, Vol. 4, No. 3 Cross Ref Perturbation analysis and condition numbers for the Tikhonov regularization of total least squares problem and their statistical estimationJournal of Computational and Applied Mathematics, Vol. 411 Cross Ref Condition numbers of multidimensional mixed least squares-total least squares problemsApplied Numerical Mathematics, Vol. 178 Cross Ref A contribution to the conditioning theory of the indefinite least squares problemsApplied Numerical Mathematics, Vol. 177 Cross Ref Condition numbers of the mixed least squares-total least squares problem revisited1 July 2022 | Linear and Multilinear Algebra, Vol. 18 Cross Ref On condition numbers of the total least squares problem with linear equality constraint1 February 2022 | Numerical Algorithms, Vol. 90, No. 1 Cross Ref Multidimensional Total Least Squares Problem with Linear Equality ConstraintsQiaohua Liu, Zhigang Jia, and Yimin Wei27 January 2022 | SIAM Journal on Matrix Analysis and Applications, Vol. 43, No. 1AbstractPDF (1051 KB)Perturbation analysis for the QX factorization for centrosymmetric matrices9 March 2020 | Linear and Multilinear Algebra, Vol. 70, No. 3 Cross Ref The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite8 February 2022 | Foundations of Computational Mathematics, Vol. 37 Cross Ref Condition Numbers for a Linear Function of the Solution to the Constrained and Weighted Least Squares Problem and Their Statistical EstimationTaiwanese Journal of Mathematics, Vol. 25, No. 4 Cross Ref Conditioning theory of the equality constrained quadratic programming and its applications30 May 2019 | Linear and Multilinear Algebra, Vol. 69, No. 6 Cross Ref Condition numbers for the K -weighted pseudoinverse and their statistical estimation20 May 2019 | Linear and Multilinear Algebra, Vol. 69, No. 4 Cross Ref Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices30 August 2020 | SeMA Journal, Vol. 78, No. 1 Cross Ref The Condition Number of Riemannian Approximation ProblemsPaul Breiding and Nick Vannieuwenhoven30 March 2021 | SIAM Journal on Optimization, Vol. 31, No. 1AbstractPDF (805 KB)Structured condition numbers and statistical condition estimation for the LDU factorization14 September 2020 | Applied Mathematics-A Journal of Chinese Universities, Vol. 35, No. 3 Cross Ref A further study on a nonlinear matrix equation1 May 2020 | Japan Journal of Industrial and Applied Mathematics, Vol. 37, No. 3 Cross Ref On the average condition number of tensor rank decompositions20 June 2019 | IMA Journal of Numerical Analysis, Vol. 40, No. 3 Cross Ref Structured condition number for multiple right-hand side linear systems with parameterized quasiseparable coefficient matrixJournal of Computational and Applied Mathematics, Vol. 368 Cross Ref Perturbation analysis of an eigenvector-dependent nonlinear eigenvalue problem with applications3 July 2019 | BIT Numerical Mathematics, Vol. 60, No. 1 Cross Ref Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian MatrixSpecial Matrices, Vol. 8, No. 1 Cross Ref On Iterative Solution of the Extended Normal EquationsHenri Calandra, Serge Gratton, Elisa Riccietti, and Xavier Vasseur8 October 2020 | SIAM Journal on Matrix Analysis and Applications, Vol. 41, No. 4AbstractPDF (563 KB)Backward error and condition number analysis for the indefinite linear least squares problem16 May 2018 | International Journal of Computer Mathematics, Vol. 96, No. 8 Cross Ref The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with ApplicationsBahar Arslan, Vanni Noferini, and Françoise Tisseur25 June 2019 | SIAM Journal on Matrix Analysis and Applications, Vol. 40, No. 2AbstractPDF (761 KB)Sensitivity Analysis of Nonlinear EigenproblemsRafikul Alam and Sk. 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