A graph technique for inverting certain matrices

Author:
B. H. Mayoh

Journal:
Math. Comp. **19** (1965), 644-646

MSC:
Primary 65.35

DOI:
https://doi.org/10.1090/S0025-5718-1965-0196924-0

MathSciNet review:
0196924

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References | Similar Articles | Additional Information

**[1]**F. Harary, "A graph theoretic approach to matrix inversion by partitioning,"*Numer. Math.*, v. 4, 1962, pp. 128-135. MR**25**#2977. MR**0139545 (25:2977)****[2]**M. Fiedler, "On inverting partitioned matrices,"*Czechoslovak. Math. J.*, v. 13 (88), 1963, pp. 574-586. (Russian summary) MR**28**#4004. MR**0160793 (28:4004)****[3]**Wai-Kai Chen, "The inversion of matrices by flow graphs,"*J. SIAM Control Ser. A.*, v. 12, 1964, pp. 676-685. MR**0171796 (30:2023)****[4]**B. H. Mayoh, "An algorithm for finding the points of attachment in a graph," submitted for publication to*Math. Scand.***[5]**L. Guttman, "Enlargement methods for computing the inverse matrix,"*Ann. Math. Statist.*, v. 17, 1948, pp. 336-343. MR**0017578 (8:171m)****[6]**H. Hotelling, "Some new methods in matrix calculation,"*Ann. Math. Statist.*, v. 14, 1943, pp. 1-34. MR**4**, 202. MR**0007851 (4:202g)****[7]**E. Bodewig, "Comparison of some direct methods for computing determinants and inverse matrices,"*Indag. Math.*, v. 9, 1947, pp. 34-42. MR**8**, 407. MR**0019403 (8:407h)****[8]**E. Bodewig,*Matrix Calculus*, North-Holland, Amsterdam, 1956. MR**18**, 235. MR**0080363 (18:235e)****[9]**G. A. Frazer, W. J. Duncan & R. A. Collar,*Elementary Matrices*, Cambridge Univ. Press, New York, 1938.**[10]**I. Schur, "Über Potenzreihe, die im Innern des Einheitskreis beschränkt sind,"*J. Reine Angew. Math.*, v. 147, 1917, pp. 205-232.**[11]**T. Banachiewicz, "Zur Berechnung der Determinanten wie auch der Inversen und zur darauf basierten Auflösung der Systeme linearer Gleichungen,"*Acta Astronomica, Sér.*v. 3, 1937, pp. 41-67.**[12]**A. S. Householder,*The Theory of Matrices in Numerical Analysis*, Blaisdell, New York, 1964. MR**0175290 (30:5475)**

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DOI:
https://doi.org/10.1090/S0025-5718-1965-0196924-0

Article copyright:
© Copyright 1965
American Mathematical Society