An Application of the Wiener-Kolmogorov Smoothing Theory to Matrix Inversion

Previous article Next article An Application of the Wiener-Kolmogorov Smoothing Theory to Matrix InversionManus FosterManus Fosterhttps: //doi. org/10. 1137/0109031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J. , 1946xvi+575 MR0016588 0063. 01014 Google Scholar2 T. N. E. Greville, The pseudoinverse of a rectangular or singular matrix and its application to the solution of systems of linear equations, SIAM Rev. , 1 (1959), 38–43 10. 1137/1001003 MR0101615 0123. 11202 LinkISIGoogle Scholar3 M. E. And Ramo, S. And Wooldridge, E. D. Grabbe, Handbook of automation, computation, and control, Vol. 1: control fundamentals, John Wiley also Automation and Remote Control, same issue (in English) MR0097281 Google Scholar9 James D. Riley, Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix, Math. Tables Aids Comput. , 9 (1955), 96–101 MR0074915 0066. 10102 CrossrefGoogle Scholar10 Claude E. Shannon and, Warren Weaver, The Mathematical Theory of Communication, The University of Illinois Press, Urbana, Ill. , 1949vi+117 MR0032134 0041. 25804 Google Scholar11 Norbert Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. With Engineering Applications, The Technology Press of the Massachusetts Institute of Technology, Cambridge, Mass, 1949ix+163, NDRC Report, Cambridge, 1942; MR0031213 0036. 09705 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Inverse Problems with I A Kronecker Structure31 July 2006 | SIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 1AbstractPDF (272 KB) Confidence Intervals for Inequality-Constrained Least Squares Problems, with Applications to Ill-Posed Problems14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 2AbstractPDF (1522 KB) Minimum-RMS Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind3 August 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 2AbstractPDF (837 KB) Volume 9, Issue 3| 1961Journal of the Society for Industrial and Applied Mathematics History Submitted: 02 November 1960Published online: 10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/0109031Article page range: pp. 387-392ISSN (print): 0368-4245ISSN (online): 2168-3484Publisher: Society for Industrial and Applied Mathematics