Some Iterative Methods for Improving Orthonormality
Zdislav V. Kovarik · SIAM Journal on Numerical Analysis · 1970
Previous article Next article Some Iterative Methods for Improving OrthonormalityZdislav KovarikZdislav Kovarikhttps://doi.org/10.1137/0707031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. K. Faddeev and , V. N. Faddeeva, Numerical Methods of Linear Algebra, SNTL, Prague, 1964 Google Scholar[2] B. C. Carlson and , Joseph M. Keller, Orthogonalization procedures and the localization of Wannier functions, Phys. Rev. (2), 105 (1957), 102–103 10.1103/PhysRev.105.102 MR0090410 0086.45102 CrossrefISIGoogle Scholar[3] V. N. Kublanovskaya, A process for improving the orthogonalization of a vector system, Zh. Vychisl. Mat. i Mat. Fiz., 5 (1965), 326–329 0189.47701 Google Scholar[4] Ky Fan and , A. J. Hoffman, Some metric inequalities in the space of matrices, Proc. Amer. Math. Soc., 6 (1955), 111–116 MR0067841 0064.01402 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Latent Variable Models15 December 2021 Cross Ref A fixed-point method for approximate projection onto the positive semidefinite coneLinear Algebra and its Applications, Vol. 523 Cross Ref Geometric multiscale decompositions of dynamic low-rank matricesComputer Aided Geometric Design, Vol. 30, No. 8 Cross Ref A Padé family of iterations for the matrix sign function and related problems25 April 2011 | Numerical Linear Algebra with Applications, Vol. 19, No. 3 Cross Ref A class of iterative methods for computing polar decompositionInternational Journal of Computer Mathematics, Vol. 88, No. 1 Cross Ref Iterative solvers for Tikhonov regularization of dense inverse problems16 August 2010 | International Journal of Computer Mathematics, Vol. 87, No. 14 Cross Ref On a stopping rule for iterative orthogonalization of symmetric matricesPAMM, Vol. 8, No. 1 Cross Ref On numerical solution of arbitrary symmetric linear systems by approximate orthogonalizationMathematics and Computers in Simulation, Vol. 79, No. 4 Cross Ref Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithmInternational Journal of Computer Mathematics, Vol. 85, No. 2 Cross Ref A new version of Kovarik's approximate orthogonalization algorithm without matrix inversionInternational Journal of Computer Mathematics, Vol. 82, No. 10 Cross Ref An iterative algorithm for approximate orthogonalisation of symmetric matricesInternational Journal of Computer Mathematics, Vol. 81, No. 2 Cross Ref Modified Kovarik Algorithm For Approximate Orthogonalization Of Arbitrary Matrices15 September 2010 | International Journal of Computer Mathematics, Vol. 80, No. 4 Cross Ref Extension of an approximate orthogonalization algorithm to arbitrary rectangular matricesLinear Algebra and its Applications, Vol. 331, No. 1-3 Cross Ref A fast Kaczmarz-Kovarik algorithm for consistent least-squares problemsKorean Journal of Computational & Applied Mathematics, Vol. 8, No. 1 Cross Ref A method for improving orthogonality of rows and columns of matricesInternational Journal of Computer Mathematics, Vol. 77, No. 3 Cross Ref Projections and preconditioning for inconsistent least-squares problemsInternational Journal of Computer Mathematics, Vol. 78, No. 4 Cross Ref Stabilizing large control linear systems on multicomputers5 August 2005 Cross Ref The matrix sign functionIEEE Transactions on Automatic Control, Vol. 40, No. 8 Cross Ref A hyperbolic tangent identity and the geometry of Padé sign function iterationsNumerical Algorithms, Vol. 7, No. 2 Cross Ref A Newton-squaring algorithm for computing the negative invariant subspace of a matrixIEEE Transactions on Automatic Control, Vol. 38, No. 8 Cross Ref On Scaling Newton's Method for Polar Decomposition and the Matrix Sign FunctionCharles Kenney and Alan J. Laub17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 3AbstractPDF (2060 KB)Polar Decomposition and Matrix Sign Function Condition EstimatesCharles Kenney and Alan J. Laub13 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 12, No. 3AbstractPDF (1503 KB)Rational Iterative Methods for the Matrix Sign FunctionCharles Kenney and Alan J. Laub17 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 2AbstractPDF (1516 KB)Fast Polar Decomposition of an Arbitrary MatrixNicholas J. Higham and Robert S. Schreiber13 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 11, No. 4AbstractPDF (817 KB)Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 Cross Ref Volume 7, Issue 3| 1970SIAM Journal on Numerical Analysis History Submitted:06 February 1969Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707031Article page range:pp. 386-389ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics