Triangular factorization and inversion by fast matrix multiplication
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- by James R. Bunch and John E. Hopcroft PDF
- Math. Comp. 28 (1974), 231-236 Request permission
Abstract:
The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in $< {C_1}{n^{{{\log }_2}7}}$ operations, and, hence, the inverse of any nonsingular matrix in $< {C_2}{n^{{{\log }_2}7}}$ operations.References
- George E. Forsythe and Cleve B. Moler, Computer solution of linear algebraic systems, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219223
- Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0175290
- Volker Strassen, Gaussian elimination is not optimal, Numer. Math. 13 (1969), 354–356. MR 248973, DOI 10.1007/BF02165411
- Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502 S. Winograd, Private communication.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 231-236
- MSC: Primary 65F30
- DOI: https://doi.org/10.1090/S0025-5718-1974-0331751-8
- MathSciNet review: 0331751