The Approximate Solution of Matrix Problems

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The Approximate Solution of Matrix Problems

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Journal of the ACM (JACM) archive
Volume 5 , Issue 3 (July 1958) table of contents

Pages: 205 - 243

Year of Publication: 1958

ISSN:0004-5411

Author

A. S. Householder

Oak Ridge National Laboratory, Oak Ridge, Tennessee

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 10, Downloads (12 Months): 50, Citation Count: 4

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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 konvexen Korper. Berlin, Julius Springer, 1934.
	2	V. N. FADDEEVA, Vycislitel'nye metody lineno~ algebry. Moscow, Gosudarstvennoe Izdatel 'stvo, 1950.
	3	MIaosLxV FIEDLER AND VLASTIMIL PTAK, Uber die Konvergenz des verallgemeinerten Seidelschen Verfahrens fur L5sung yon Systemen liuearer Gleichungen. Math. Nachr. 15 (1956), 31-38.
	4	G. FROnENIUS, Uber Matrizen aus positiven Elementen. Berlin Sitz. (1908) 471-76, (1909) 514-18.
	5	_______ Uber Matrizen aus nicht negativen Elementen. Berlin Sitz. (1912), 456-77
	6	A. DE LA GARZA, Error bounds on approximate solutions to systems of linear algcbraic equations. MTAC 7 (1953), 81-84.
	7	AIJSTON S. HOUSEHOLDER, Principles of numerical analysis. New York, McGraw-Hill 1953.
	8	_____,On the convergence of matrix iterations. Oak Ridge National Laboratory, ORNL-1883, 1955.
	9	Alston S. Householder, On the Convergence of Matrix Iterations, Journal of the ACM (JACM), v.3 n.4, p.314-324, Oct. 1956 [doi>10.1145/320843.320851]
	10	______, Generated error in the solution of certain partial difference equations. Oak Ridge National Laboratory, ORNL-2230, 1956.
	11	A. KOLMOGOROFF, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes. Studia Math. 5 (1934), 29533.
	12	N. S. MENDELSOHN, Some elementary properties of ill-conditioned matrices and linear equations. CARDE Technical Memorandum No. 120/55, 1955.
	13	A . R. MITCHELL, Itound-off errors in implicit finite difference methods. Qu. J. Mech. Appl. Math. 9 (1956), 111-21.
	14	RICHARD VON MISES AND HILDA POLLACZEK-GEIRINGER, Praktische Verfahren der Matrixaufl6sung, Z. angew. Mat. Mech. 9 (1929), 58-77, 152-64.
	15	John V0N NEUMANN, Some matrix inequalities and mctrization of matrixrspace. Bull. 1nat. Math. Mech. Univ. Tomsk 1 (1937), 286-99.
	16	Jou~ YON NEUMANN AND HERMAN GOLDSTINE, Numerical inverting of matrices of high order. Bull. Am. Math. Soc. 53 (1947), 1021-99.
	17	RUFUS OLDENBVRGER, infinite powers of matrices and characteristic roots. Duke Math. J. 6(1940), 357-61.
	18	ALEXANDER OSTROWSKI, Uber Normen yon Matrizen, Math. Z. 68 (1955), 2-18.
	19	EDGAR REICH, On the convergence of the classical iterative method of solving linear simultaneous equations. Ann. Math. Star. 20 (1949), 448-51.
	20	D. E. RUTHERFORD, Some eontinuant determinants arising in physics and chemistry. Prec. Roy. 8oc. Edinburgh A 62 (1945), 229-36, 65 (1951), 232-41.
	21	P. STEIN, Some general theorems on iterants. J. Res. Natl. Bur. Stand. 48 (1952), 82- 83.
	22	________, AND R. L. ROSENBERG, On the solution of linear simultaneous equations by iteration. J. London Math. Sac. 23 (1948), 111-18.
	23	JOHN TODD, A direct approach to the problem of stability iv. the numerical solution of partiM differentiM equations. Comm. Pure and Appl. Math. 9 (1956), 597-612.
	24	JOHANNES WEISSINGER, Uber das Iterationsveffahren Z. angew. Math. Mech. 31 (1951), 245-46.
	25	______, Zur Theorie und Anwendung des iterationsverfahrens. Math. Nachr. 8 (1952), 193-212.
	26	______, Verallgemeinerung des Seidelschen Iterationsverfahrens. Z. angew. Math. Mech. ~3 (1953), 155-63.
	27	HELMUT WIELANDT, Unzerlegbare nichtnegative Matrizen. Math. Z. 52 (1950), 642-48.
	28	DAVID YOUNG, Iterative methods for solving partial dlfference equations of elliptic type. Tranv. Amer. Math. Soc. 76 (1954), 92-111.

CITED BY 4

	J. W. Sheldon, On the Spectral Norms of Several Iterative Processes, Journal of the ACM (JACM), v.6 n.4, p.494-505, Oct. 1959
	E. E. Osborne, On Least Squares Solutions of Linear Equations, Journal of the ACM (JACM), v.8 n.4, p.628-636, Oct. 1961
	E. E. Osborne, On Pre-Conditioning of Matrices, Journal of the ACM (JACM), v.7 n.4, p.338-345, Oct. 1960
	E. E. Osborne, On pre-conditioning matrices, Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery, September 01-03, 1959, Cambridge, Massachusetts