Petryshyn, W. V. On generalized inverses and on the uniform convergence of \((I-\beta K)_ n\) with application to iterative methods. (English) Zbl 0189.47502 J. Math. Anal. Appl. 18, 417-439 (1967). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 32 Documents Keywords:numerical analysis PDF BibTeX XML Cite \textit{W. V. Petryshyn}, J. Math. Anal. Appl. 18, 417--439 (1967; Zbl 0189.47502) Full Text: DOI References: [1] Moore, E. H., On the reciprocal of the general algebraic matrix, Bull. Amer. Math. Soc., 26, 394-395 (1920), (Abstract) [2] Moore, E. H., General analysis, Mem. Amer. Phil. Soc., I (1935), Part I · JFM 61.0433.06 [3] Penrose, R., On a generalized inverse for matrices, (Proc. Cambridge Phil. Soc., 51 (1955)), 406-413, Part 3 · Zbl 0065.24603 [4] Bjerhammer, A., Rectangular reciprocal matrices with special reference to geodesic calculations, Bull. Geodesigue, 188-220 (1951) [5] Greville, T. N.E, Some application of the pseudoinverse, SIAM Rev., 2, 15-22 (1960) · Zbl 0168.13303 [6] Kalman, R. E., New methods and results in linear prediction and filtering theory, (RIAS Techn. Rep. 61-1 (1960), Purdue University) · Zbl 0218.93019 [7] Kalman, R. E.; Ho, Y. C.; Narenda, K. S., Controllability of linear dynamic systems, (Contrib. Diff. Eqs., Vol. I (1962), Wiley (Interscience): Wiley (Interscience) New York) · Zbl 0151.13303 [8] Price, C. M., The matrix pseudoinverse and minimal variance estimates, SIAM Rev., 6, 115-120 (1964) · Zbl 0125.37202 [9] Pyle, L. D., Generalized inverse computations using the gradient projection method, J. ACM, 11, 422-428 (1964) · Zbl 0123.11203 [10] Rosen, J. B., The gradient projection method for nonlinear programming. Part I: Linear constraints, J. SIAM, 8, 181-217 (1960) · Zbl 0099.36405 [11] Ben-Israel, A.; Charnes, A., Contributions to the theory of generalized inverses, J. SIAM, 11, 667-699 (1963) · Zbl 0116.32202 [13] Beutler, F. J., The operator theory of the pseudo-inverse I: bounded operators, J. Math. Anal. Appl., 10, 451-470 (1965) · Zbl 0151.19205 [14] Decell, H. P., An alternate form of the generalized inverse of an arbitrary complex matrix, SIAM Rev., 7, 356-358 (1965) · Zbl 0131.01502 [15] Desoer, C. A.; Whalen, B. H., A note on pseudoinverses, J. SIAM, 11, 442-447 (1963) · Zbl 0123.09603 [16] Greville, T. N.E, The pseudoinverse of a rectangular or singular matrix and its applications to the solution of systems of linear equations, SIAM Rev., 1, 38-43 (1959) · Zbl 0123.11202 [17] Hestenes, M. R., Inversion of matrices by biorthogondization and related results, J. SIAM, 6, 84 (1958) [18] Osborne, E. E., On least squares solutions of linear equations, J. ACM, 8, 628-638 (1961) · Zbl 0115.34304 [20] Ben-Israel, A., An iterative method for computing the generalized inverse of an arbitrary matrix, Math. Comp., 19, 452-455 (1965) · Zbl 0136.12703 [22] Ben-Israel, A.; Wersan, S. J., An elimination method for computing the generalized inverse of an arbitrary complex matrix, J. ACM, 10, 532-537 (1962) · Zbl 0118.12104 [23] Boot, J. C.G, The computation of the generalized inverse of singular or rectangular matrices, Amer. Math. Month., 70 (1963) · Zbl 0112.01203 [24] Kublanovskaya, V. N., On the computation of the generalized matrix inverse and the projection, J. Comp. Math. Phys., 6, 326-332 (1966) [25] Altman, M., Approximation methods in functional analysis, (Lecture Notes (1959), California Institute of Technology) · Zbl 0118.11901 [26] Bialy, H., Iterative Behandlung linearer Funktionalgleichungen, Arch. Rat. Mech. Anal., 4, 166-176 (1959) · Zbl 0154.40204 [27] Browder, F. E.; Petryshyn, W. V., The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc., 72, 566-570 (1966) · Zbl 0138.08201 [28] Petryshyn, W. V., On the inversion of matrices and linear operators, (Proc. Amer. Math. Soc., 16 (1965)), 893-901 · Zbl 0151.19301 [29] Petryshyn, W. V., On the convergence of an accelerated iterative method in the solution of singular equations, (ICR Quarterly Rep. No. 9 (1966), University of Chicago) · Zbl 0111.31701 [30] Gohberg, I. C.; Krein, M. G., Fundamental aspects of defect numbers, root numbers and indices of linear operators, Uspehi Mat. Nauk, 12, 43-118 (1957) · Zbl 0088.32101 [31] Taylor, A. E., Introduction to Functional Analysis (1958), Wiley: Wiley New York · Zbl 0081.10202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.