Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix

Author:
James D. Riley

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

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References | Similar Articles | Additional Information

**[1]**M. Herzberger,*The normal equations of the method of least squares and their solution*, Quart. Appl. Math.**7**(1949), 217–223. MR**0030815**, https://doi.org/10.1090/S0033-569X-1949-30815-5**[2]**F. S. Shaw,*An introduction to relaxation methods*, Dover Publications, Inc., New York., N.Y., 1953. MR**0058303****[3]**Olga Taussky,*Notes on numerical analysis. II. Note on the condition of matrices*, Math. Tables and Other Aids to Computation**4**(1950), 111–112. MR**0038137**, https://doi.org/10.1090/S0025-5718-1950-0038137-8**[4]**H. Polachek,*On the solution of systems of linear equations of high order*, Rep. NOLM-9522, Naval Ordnance Laboratory, White Oak, Md., 1948. MR**0035115****[5]**A. C. Aitken, ``On Bernoulli's numerical solution of algebraic equations,'' Roy. Soc., Edinburgh,*Proc.*, v. 46, 1926, p. 289-305.**[6]**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**0036086****[7]**Daniel Shanks,*Non-linear transformations of divergent and slowly convergent sequences*, J. Math. and Phys.**34**(1955), 1–42. MR**0068901**, https://doi.org/10.1002/sapm19553411**[8]**George E. Forsythe,*Solving linear algebraic equations can be interesting*, Bull. Amer. Math. Soc.**59**(1953), 299–329. MR**0056372**, https://doi.org/10.1090/S0002-9904-1953-09718-X**[9]**John von Neumann and H. H. Goldstine,*Numerical inverting of matrices of high order*, Bull. Amer. Math. Soc.**53**(1947), 1021–1099. MR**0024235**, https://doi.org/10.1090/S0002-9904-1947-08909-6**[10]**G. H. Hardy, J. E. Littlewood, & G. Pólya,*Inequalities*, Cambridge, 1934.**[11]**Kenneth Levenberg,*A method for the solution of certain non-linear problems in least squares*, Quart. Appl. Math.**2**(1944), 164–168. MR**0010666**, https://doi.org/10.1090/qam/10666

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DOI:
https://doi.org/10.1090/S0025-5718-1955-0074915-1

Article copyright:
© Copyright 1955
American Mathematical Society