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On the inversion of matrices and linear operators


Author: W. V. Petryshyn
Journal: Proc. Amer. Math. Soc. 16 (1965), 893-901
MSC: Primary 65.10
DOI: https://doi.org/10.1090/S0002-9939-1965-0182121-3
MathSciNet review: 0182121
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  • [1] J. Albrecht, Bemerkungen zum Iterationsverfahren von Schulz zur Matrixinversion, Z. Angew. Math. Mech. 41 (1961), 262-263. MR 0128605 (23:B1644)
  • [2] M. Altman, An optimum cubically convergent iterative method of inverting a linear bounded operator in Hilbert space, Pacific J. Math. 10 (1960), 1107-1113. MR 0126165 (23:A3461)
  • [3] R. Ansorge, Über ein Iterationsverfahren von G. Schulz zur Ermittlung der Reziproken einer Matrix, Z. Angew. Math. Mech. 39 (1959), 164-165. MR 0128606 (23:B1645)
  • [4] W. Dück, Fehlerabschätzungen für das Iterationsverfahren von Schulz zur Bestimmung der Inversen einer Matrix, Z. Angew. Math. Mech. 40 (1960), 192-194. MR 0112248 (22:3102)
  • [5] F. John, Advanced numerical analysis, Lecture Notes, Institute of Math. Sci., New York University, 1956.
  • [6] H. Hotelling, Some new methods in matrix calculation, Amer. Math. Statist. 14 (1943), 1-34. MR 0007851 (4:202g)
  • [7] M. Newman, Matrix computations, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 222-254. MR 0149654 (26:7139)
  • [8] W. V. Petryshyn, On the generalized overrelaxation method for operator equations, Proc. Amer. Math. Soc. 14 (1963), 917-924. MR 0169402 (29:6652)
  • [9] -, On a class of K-p.d. and non-K-p.d. operators and operator equations, J. Math. Anal. Appl. 10 (1965), 1-24. MR 0216306 (35:7141)
  • [10] -, On extrapolated Jacobi or simultaneous displacements method in the solution of matrix and operator equations, Math. Comp. 19 (1965), 37-55 MR 0176601 (31:873)
  • [11] G. Schulz, Iterative Berechnung der reziproken Matrix, Z. Angew. Math. Mech. 13 (1933), 57-59.
  • [12] A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1957. MR 0098966 (20:5411)

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DOI: https://doi.org/10.1090/S0002-9939-1965-0182121-3
Article copyright: © Copyright 1965 American Mathematical Society

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