The Jacobi Method for Real Symmetric Matrices

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The Jacobi Method for Real Symmetric Matrices

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Journal of the ACM (JACM) archive
Volume 6 , Issue 1 (January 1959) table of contents

Pages: 59 - 96

Year of Publication: 1959

ISSN:0004-5411

Authors

H. H. Goldstine	International Business Machines Corporation, Yorktown, N.Y.
F. J. Murray	Columbia University, New York, N.Y.
J. von Neumann

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 7, Downloads (12 Months): 69, Citation Count: 7

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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	E. BODEWIG, On Graeffe's meihod for solving algebraic equations, Quart. Appl. Math. 4 (1946), 177-190.
	2	BARGMANN, MONTGOIERY AND VON NEUMANN, Solution of linear systems of high order, Institute for Advanced Study, 25 October 1946.
	3	COURnNT-HH,BERT, Methoden der Mathematischen Physik, vol. I, Berlin, 1931.
	4	G. t.. FORSYTHE AND P. HENaICI, The cyclic Jacobi method for computing the principal values of tL eomplex matrix. To be published.
	5	T. C. FRY, Some numerical methods for locating roots of polynomials, Quart. Appl. Math. 3 (1945), 89-105.
	6	W. GIVENS, NumericM computation of the characteristic values of a real symmetric matrix, Otk Ridge National Laboratory, ORNL-1574, 1954.
	7	R. T. GrmQmY, Computing eigenvalues ttnd eigenvecLors, Math. Tables Aids Comp. 7 (1953), 215-220.
	8	C. G. J. JACOBI, bcr ein leichtes Verfhren, die in dcr Thcorie der SScularsorungen vorkomnmnden Geichungen nuraerisch "ufzulSsen, J. reine angew. Math. 80 (1846), 51-95.
	9	W. M. KINCAID, Numerical methods for finding characteristic roots and vectors of matrices, Quart. Appl. Malh. 5 (1947-1948), 320-345.
	10	David A. Pope , C. Tompkins, Maximizing Functions of Rotations—Experiments Concerning Speed of Diagonalization of Symmetric Matrices Using Jacobi's Method, Journal of the ACM (JACM), v.4 n.4, p.459-466, Oct. 1957 [doi>10.1145/320893.320901]
	11	A. L. TURING, On computable numbers with an application to the Entscheidungs problem, Proc. London Math. Soc. Set. 2, 42 (1936-37), 230-285.
	12	J. VON NEUMANN AND H. I. GOLDSTINE, Numerical inverting of matrices of high order, Bull. Amer. Malh. Soc. 58 (1947), 1021-1099.
	13	H. WAYLAND, Expansion of determinental equations into polynomial form, Quart. Appl. Math. 2 (1945), 277--306.
	14	WIIITAKER AND ROBINSON, Calculus of Observations, Bbckie aml Son, Ltd., London, 1937, pp. 78-131.f

CITED BY 7

	H. H. Goldstine, Footnote to a Recent Paper, Journal of the ACM (JACM), v.7 n.1, p.78-79, Jan. 1960
	F. J. Corbató, On the Coding of Jacobi's Method for Computing Eigenvalues and Eigenvectors of Real Symmetric Matrices, Journal of the ACM (JACM), v.10 n.2, p.123-125, April 1963
	F. J. Corbató, On the coding of Jacobi's method of computing eigenvalues and eigenvectors of real, symmetric matrices, Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery, September 01-03, 1959, Cambridge, Massachusetts
	Lei Zou , Lei Chen , Jeffrey Xu Yu , Yansheng Lu, A novel spectral coding in a large graph database, Proceedings of the 11th international conference on Extending database technology: Advances in database technology, March 25-29, 2008, Nantes, France
	G. Estrin , C. R. Viswanathan, Organization of a ``Fixed-Plus-Variable'' Structure Computer for Computation of Eigenvalues and Eigenvectors of Real Symmetric Matrices, Journal of the ACM (JACM), v.9 n.1, p.41-60, Jan. 1962
	William K. Winters, A Modified Method of Latent Class Analysis for File Organization in Information Retrieval, Journal of the ACM (JACM), v.12 n.3, p.356-363, July 1965
	H. H. Goldstine , L. P. Horwitz, A Procedure for the Diagonalization of Normal Matrices, Journal of the ACM (JACM), v.6 n.2, p.176-195, April 1959