Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix
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- by James D. Riley PDF
- Math. Comp. 9 (1955), 96-101 Request permission
References
- M. Herzberger, The normal equations of the method of least squares and their solution, Quart. Appl. Math. 7 (1949), 217–223. MR 30815, DOI 10.1090/S0033-569X-1949-30815-5
- F. S. Shaw, An introduction to relaxation methods, Dover Publications, Inc., New York, N.Y., 1953. MR 0058303
- Olga Taussky, Notes on numerical analysis. II. Note on the condition of matrices, Math. Tables Aids Comput. 4 (1950), 111–112. MR 38137, DOI 10.1090/S0025-5718-1950-0038137-8
- H. Polachek, On the solution of systems of linear equations of high order, Naval Ordnance Laboratory, White Oak, Md., 1948. Rep. NOLM-9522,. MR 0035115 A. C. Aitken, “On Bernoulli’s numerical solution of algebraic equations,” Roy. Soc., Edinburgh, Proc., v. 46, 1926, p. 289-305.
- A. C. Aitken, Studies in practical mathematics. V. On the iterative solution of a system of linear equations, Proc. Roy. Soc. Edinburgh Sect. A 63 (1950), 52–60. MR 36086
- Daniel Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1–42. MR 68901, DOI 10.1002/sapm19553411
- George E. Forsythe, Solving linear algebraic equations can be interesting, Bull. Amer. Math. Soc. 59 (1953), 299–329. MR 56372, DOI 10.1090/S0002-9904-1953-09718-X
- John von Neumann and H. H. Goldstine, Numerical inverting of matrices of high order, Bull. Amer. Math. Soc. 53 (1947), 1021–1099. MR 24235, DOI 10.1090/S0002-9904-1947-08909-6 G. H. Hardy, J. E. Littlewood, & G. Pólya, Inequalities, Cambridge, 1934.
- Kenneth Levenberg, A method for the solution of certain non-linear problems in least squares, Quart. Appl. Math. 2 (1944), 164–168. MR 10666, DOI 10.1090/S0033-569X-1944-10666-0
Additional Information
- © Copyright 1955 American Mathematical Society
- Journal: Math. Comp. 9 (1955), 96-101
- MSC: Primary 65.0X
- DOI: https://doi.org/10.1090/S0025-5718-1955-0074915-1
- MathSciNet review: 0074915