On the Convergence of Matrix Iterations

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On the Convergence of Matrix Iterations

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Journal of the ACM (JACM) archive
Volume 3 , Issue 4 (October 1956) table of contents

Pages: 314 - 324

Year of Publication: 1956

ISSN:0004-5411

Author

Alston S. Householder

Oak Ridge National Laboratory, Oak Ridge, Tenn.

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 8, Downloads (12 Months): 64, Citation Count: 3

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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	T. BONNESEN AND W. FENCHEL, Theorie der knovexen Ktrper. Berlin, Julius Springer, 1934.
	2	ALBERT H. B0WKER, On the norm of a matrix. An. Math. Slat. 18 (1947) 285-8.
	3	ALFRED BAUER, Limits for the characteristic roots of a matrix. Duke Math. Jour. 13 (1946) 387-95; 14 (1947) 21-26; 15 (1948) 871-77.
	4	V. N. FADIEEVA, Vyislitel'nye melody lineinoi algebry, Moscow and Leningrad, Gosudarstvennoe Izdatel'stvo Tehnikoteoi,,etieskai literatury, 1950.
	5	C. FOBENIUS, t3ber Matrizen aus positiven Elementen. Berlin Sitz. (1908) 471-76, (1909) 514-18.
	6	uber Matrizen aus nicht negativen Elementen. Berlin Sitz. (1912) 456-77.
	7	A. DE IA GARZA, Error bounds on approximate solutions to systems of linear algebraic equations. MTAC 7 (1953) 81-84
	8	HILDA GEIRINGER, On the solution of systems of linear equations by certain iteration methods. Reissner Anniversary Volume, Ann Arbor, J. W. Edwards (1949) 365-93.
	9	ALSTON S. HOUSEHOLDER, Principles o} numerical analysis. New York, McGraw-Hill, 1953.
	10	_, On norms of vectors and matrices. Oak Ridge National Laboratory, ORNL-1756, Physics, 1954.
	11	On the convergence of matrix iterations. Oak Ridge National Laboratory, ORNL- 1883, Physics, 1955.
	12	R. V. Mms AND H. POLLACZEK-GEIRINOER, Praktische Verfahren der GleichungsauflSsung. Z. Angew. Math u. Mech. 9 (1929) 58-77, 152--64.
	13	JohN yon N,UANN, Some matrix inequalities and metrization of matrix-space, Bull. Inst. Math. Mech. Univ. Tomsk (1937) 286-99.
	14	RUFUS OLDENBURGER, Infinite powers of matrices and characteristic roots. Duke Math. Jour 6 (1940) 357-61.
	15	OSKAR PERRON, Algebra II, Theorie der algebraischen Gleichungen. Berlin, Walter de Gruyter, 1951.
	16	EDGAR REICH, On the convergence of the classical iterative method of solving linear simultaneous equations. Ann Math. Slat. 20 (1949) 448-51.
	17	P. STEIN AND R. L. ROSENBERG, 0n the solution of linear simultaneous equations by iteration. J. London Math. Soc. 23 (1948) 111-18.
	18	JOHANNES WEISSINGER, Zur Theorie und Anwendung des Iter,tionsverfahrens. Math. Naeh. 8 (1952) 193-212.
	19	HELMUT WIELXNDT, Unzerlegbare, nicht negative Matrizcn. Malh. Zeit. 52 (1950) 642-48.

CITED BY 3

	Alston S. Householder, Generated error in the solution of certain linear difference equations, Proceedings of the 1956 11th ACM national meeting, p.52-55, January 1956
	Susie E. Atta, Effect of Propagated Error on Inverse of Hilbert Matrix, Journal of the ACM (JACM), v.4 n.1, p.36-40, Jan. 1957
	A. S. Householder, The Approximate Solution of Matrix Problems, Journal of the ACM (JACM), v.5 n.3, p.205-243, July 1958