Error Analysis of Direct Methods of Matrix Inversion

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Error Analysis of Direct Methods of Matrix Inversion

Full text

Pdf (1.92 MB)

Source

Journal of the ACM (JACM) archive
Volume 8 , Issue 3 (July 1961) table of contents

Pages: 281 - 330

Year of Publication: 1961

ISSN:0004-5411

Author

J. H. Wilkinson

National Physical Laboratory, Teddington, England

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 30, Downloads (12 Months): 161, Citation Count: 28

Additional Information:

references cited by index terms collaborative colleagues

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/321075.321076 What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BAUER, F. :L. Sequential reduction to tridiagonaI form J. Soc. Indust. Appl. Math. 7 (1959), 107.
	2	GIVENS, W. The hnear equations problem Technical Report no. 3. Applied Mathematics and Statistics Series, Nonr 225 (37). Stanford University, 1959.
	3	GOLDSTINE~ }:t. H.; AND VON NEUMANN, J. Numerical inverting of matrices of high order. B~ll. Amer. Math. Soc. 53 (1947), 1021.
	4	Alston S. Householder, Unitary Triangularization of a Nonsymmetric Matrix, Journal of the ACM (JACM), v.5 n.4, p.339-342, Oct. 1958 [doi>10.1145/320941.320947]
	5	RVTISHAUS~R, H. Solution of eigenvalue problems with the L-R transformation. In National Bureau of Standards Apphed Math Series 49 (1958).
	6	Tvm~(~, A.M. Rounding-off errors in matrix processes. Quart. J. Mech. A ppl. Math. I (1948), 287.
	7	WIT~NSON, J. H. Rounding errors in algebraic processes. Proceedings of International Conference on Information Processing, UNESCO, 1959.
	8	WILKINSON, J, H. Error analysis of floating-point computation. Num Math ~ (1960), 319
	9	FADD~VA, V. N. Computational methods of hnear algebra. (Translated by C. D. Benster.) New York: Dover; London. Constable, 1959.

CITED BY 28

	B. N. Parlett, J. H. Wilkinson's work and influence on matrix computations, Proceedings of the ACM conference on History of scientific and numeric computation, p.133-138, May 13-15, 1987, Princeton, New Jersey, United States
	A. C. McKellar , E. G. Coffman, Jr., Organizing matrices and matrix operations for paged memory systems, Communications of the ACM, v.12 n.3, p.153-165, March 1969
	G. Peters , J. H. Wilkinson, On the stability of Gauss-Jordan elimination with pivoting, Communications of the ACM, v.18 n.1, p.20-24, Jan. 1975
	A. Colker, Algorithm 184: Erlang probalility for curve fitting, Communications of the ACM, v.6 n.7, p.386, July 1963
	H. H. Wang, A Parallel Method for Tridiagonal Equations, ACM Transactions on Mathematical Software (TOMS), v.7 n.2, p.170-183, June 1981
	Realizing Boolean connectives on the IBM 1620, Communications of the ACM, v.6 n.7, p.385, July 1963
	R. P. van de Riet, Algorithm 187: differences and derivatives, Communications of the ACM, v.6 n.7, p.387, July 1963
	V. W. Whitley, Algorithm 129: Minifun, Communications of the ACM, v.5 n.11, p.550-551, Nov. 1962
	Jules J. Lambiotte, Jr. , Robert G. Voigt, The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer, ACM Transactions on Mathematical Software (TOMS), v.1 n.4, p.308-329, Dec. 1975
	Peter G. Behrenz, Algorithm 133: Random, Communications of the ACM, v.5 n.11, p.553, Nov. 1962
	Nai-kuan Tsao, Some a Posteriori Error Bounds in Floating-Point Computations, Journal of the ACM (JACM), v.21 n.1, p.6-17, Jan. 1974
	Cleve Moler, Remark on certification of matrix inversion procedures, Communications of the ACM, v.6 n.7, p.389, July 1963
	J. J. Du Croz , S. M. Nugent , J. K. Reid , D. B. Taylor, Solving Large Full Sets of Linear Equations in a Paged Virtual Store, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.527-536, Dec. 1981
	Bruce A. Chartres , James C. Geuder, Computable Error Bounds for Direct Solution of Linear Equations, Journal of the ACM (JACM), v.14 n.1, p.63-71, Jan. 1967
	Henry C. Thacher, Jr., Certification of algorithms 134 and 158 exponentiation of series, Communications of the ACM, v.6 n.7, p.390, July 1963
	G. W. Stewart, III , Dale W. Lick, Numerical Analysis: Numerical solution of a thin plate heat transfer problem, Communications of the ACM, v.11 n.9, p.639-640, Sept. 1968
	Richard H. Bartels , Gene H. Golub, Numerical Analysis: Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations, Communications of the ACM, v.11 n.6, p.401-406, June 1968
	Y. Charlie Hu , Guohua Jin , S. Lennart Johnsson , Dimitris Kehagias , Nadia Shalaby, HPFBench: a high performance Fortran benchmark suite, ACM Transactions on Mathematical Software (TOMS), v.26 n.1, p.99-149, March 2000
	G. w. Stewart, The Decompositional Approach to Matrix Computation, Computing in Science and Engineering, v.2 n.1, p.50-59, January 2000
	Charles S. Kenney , B. S. Manjunath , Marco Zuliani , Gary A. Hewer , Alan Van Nevel, A Condition Number for Point Matching with Application to Registration and Postregistration Error Estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.25 n.11, p.1437-1454, November 2003
	James R. Bunch, Equilibration of Symmetric Matrices in the Max-Norm, Journal of the ACM (JACM), v.18 n.4, p.566-572, Oct. 1971
	A. P. Relph, Algorithm 190: complex power, Communications of the ACM, v.6 n.7, p.388, July 1963
	Daniel Boley , Gene H. Golub , Samy Makar , Nirmal Saxena , Edward J. McCluskey, Floating Point Fault Tolerance with Backward Error Assertions, IEEE Transactions on Computers, v.44 n.2, p.302-311, February 1995
	T. A. Davis , E. S. Davidson, Pairwise Reduction for the Direct, Parallel Solution of Sparse, Unsymmetric Sets of Linear Equations, IEEE Transactions on Computers, v.37 n.12, p.1648-1654, December 1988
	V. Cortés , J. M. Peña, Growth factor and expected growth factor of some pivoting strategies, Journal of Computational and Applied Mathematics, v.202 n.2, p.292-303, May, 2007
	P. Alonso , J. Delgado , R. Gallego , J. M. Pena, Iterative refinement for Neville elimination, International Journal of Computer Mathematics, v.86 n.2, p.341-353, February 2009
	Chi-Ye Wu , Ting-Zhu Huang, Stability of block LU factorization for block tridiagonal matrices, Computers & Mathematics with Applications, v.57 n.3, p.339-347, February, 2009
	G. A. Sitton, Direct technique for improving a matrix inverse, IBM Journal of Research and Development, v.15 n.5, p.413-417, September 1971