Cited By
View all- He J(2016)An analytic expression of relative approximation error for a class of evolutionary algorithms2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7744345(4366-4373)Online publication date: Jul-2016
An efficient algorithm for computing powers of triangular matrices
Author: 
C. P. HuangAuthors Info & Claims
C. P. HuangAuthors Info & ClaimsPages 954 - 957
Abstract
An efficient algorithm for the computation of powers of a square arbitrary lower triangular matrix is presented. A comparison of the algorithm with the standard matrix multiplication method in terms of maximum number of multiplications is included. A numerical example is used to show some of the computational details.
References
[1]
Brent, R. P., Algorithms for matrix multiplications, Tech. Rep. of the Comput. Sci. Dept., Stanford Univ., Stanford, Calif., pp. 70-157 (1970).
[2]
Brockett, R. W. and Dobkin, D., On the number of multiplications required for matrix multiplication, SIAM J. Comput., 5, pp. 624-628 (1976).
[3]
Datta, B. N. and Datta K., An algorithm for computing powers of a Hessenberg matrix and its applications, Linear Algebra Appl., 14, pp. 273-284 (1976).
[4]
Huang, C. P., Computing powers of arbitrary Hessenberg matrices, Linear Algebra Appl (to appear).
[5]
Parlett, B. N., A recurrence among the elements of functions of triangular matrices, Linear Algebra Appl., 14, pp. 117-121 (1976).
[6]
Stewart, G. W., Introduction to Matrix Computations, (Academic Press, 1973).
[7]
Winograd, S., A new algorithm for inner-product, IEEE Trans. Comput., 17, pp. 693-694 (1968).
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- An efficient algorithm for computing powers of triangular matrices
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Published In
January 1978
990 pages
Copyright © 1978 ACM.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 01 January 1978
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View all- He J(2016)An analytic expression of relative approximation error for a class of evolutionary algorithms2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7744345(4366-4373)Online publication date: Jul-2016
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