Generalized Inverses and Generalized Green’s Functions
Warren S. Loud · SIAM Journal on Applied Mathematics · 1966
Previous article Next article Generalized Inverses and Generalized Green’s FunctionsW. S. LoudW. S. Loudhttps://doi.org/10.1137/0114030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Ben-Israel and , A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math., 11 (1963), 667–699 10.1137/0111051 MR0179192 0116.32202 LinkISIGoogle Scholar[2] R. Courant and , D. Hilbert, Methoden der Mathematischen Physik, Vol. I, Springer, Berlin, 1931, Chap. 5, 14 0001.00501 CrossrefGoogle Scholar[3] 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[4] T. N. E. 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Soc., 52 (1956), 17–19 MR0074092 0070.12501 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Green’s matrices for the BVP for the system of ODE of the first order: applications to the beam theories3 July 2017 | Archive of Applied Mechanics, Vol. 87, No. 10 Cross Ref On the Conditioning of Multipoint and Integral Boundary Value Problems17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 20, No. 1AbstractPDF (1049 KB)Generalized inverses of matrices: a perspective of the work of Penrose24 October 2008 | Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 100, No. 3 Cross Ref Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 Cross Ref A Bifurcation Application of the Generalized Inverse of a Linear Differential Operator17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 11, No. 3AbstractPDF (1456 KB)Operators on Banach spaces with complemented rangesActa Mathematica Academiae Scientiarum Hungaricae, Vol. 35, No. 1-2 Cross Ref Splittings and iterative methods for approximate solutions to singular operator equations in Hilbert spacesJournal of Mathematical Analysis and Applications, Vol. 62, No. 2 Cross Ref The Generalized Green's Function for Regular Ordinary Differential Subspaces in L2[a,b] ⊕ L2[a,b] Cross Ref The generalized Green’s function for an 𝑛th order linear differential operator1 January 1977 | Transactions of the American Mathematical Society, Vol. 228, No. 0 Cross Ref Annotated Bibliography on Generalized Inverses and Applications Cross Ref Generalized Green's functions and generalized inverses for linear differential systems with Stieltjes boundary conditionsJournal of Differential Equations, Vol. 16, No. 2 Cross Ref The problem of generalized Green matricesMathematical Notes of the Academy of Sciences of the USSR, Vol. 15, No. 1 Cross Ref Use of Green's functions in the numerical solution of two-point boundary value problems27 August 2006 Cross Ref Generalized Green’s Matrices for Linear Differential Systems17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 4, No. 1AbstractPDF (581 KB)Iterative methods for best approximate solutions of linear integral equations of the first and second kindsJournal of Mathematical Analysis and Applications, Vol. 40, No. 3 Cross Ref On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 1AbstractPDF (1764 KB)Das verallgemeinerte Inverse eines linearen Operators in Vektorräumen mit nicht ausgearteter Hermitescher Metrik über einenm kommutativen Körper.Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1972, No. 252 Cross Ref Generalized Inverses, Normal Solvability, and Iteration for Singular Operator Equations Cross Ref A Restricted Pseudoinverse and Its Application to Constrained MinimaNariyasu Minamide and Kahei Nakamura12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 19, No. 1AbstractPDF (910 KB)Some Examples of Generalized Green’s Functions and Generalized Green’s Matrices18 July 2006 | SIAM Review, Vol. 12, No. 2AbstractPDF (1401 KB)Some Remarks on Hermitian and Anti-Hermitian Properties of Green’s MatricesJames S. 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