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 SectionsAbout[1] Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946xvi+575 MR0016588 0063.01014 Google Scholar[2] 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 Scholar[3] M. E. And Ramo, S. And Wooldridge, E. D. Grabbe, Handbook of automation, computation, and control, Vol. 1: control fundamentals, John Wiley & Sons Inc., New York, 1958xx+999 MR0095591 0093.09401 Google Scholar[4] A. Kolmogoroff, Interpolation und Extrapolation von stationären zufälligen Folgen, Bull. Acad. Sci. URSS Sér. Math. [Izvestia Akad. Nauk. SSSR], 5 (1941), 3–14 MR0004416 0024.15901 Google Scholar[5] Kenneth Levenberg, A method for the solution of certain non-linear problems in least squares, Quart. Appl. Math., 2 (1944), 164–168 MR0010666 0063.03501 CrossrefGoogle Scholar[6] E. H. Moore, General Analysis, Mem. Amer. Philos. Soc., Vol. 1, 19358 and Ch. 3 0013.11605 Google Scholar[7] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[8] V. S. Pugačev, Determination of optimal system in terms of a general criterion, Avtomat. i Telemeh., 19 (1958), 519–539, (in Russian) ; also Automation and Remote Control, same issue (in English) MR0097281 Google Scholar[9] 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 Scholar[10] Claude E. Shannon and , Warren Weaver, The Mathematical Theory of Communication, The University of Illinois Press, Urbana, Ill., 1949vi+117 MR0032134 0041.25804 Google Scholar[11] 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