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Bounds for the error of linear systems of equations using the theory of moments. (English) Zbl 0238.65012


MSC:

65F10 Iterative numerical methods for linear systems
65F05 Direct numerical methods for linear systems and matrix inversion
65F99 Numerical linear algebra
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References:

[1] Aheizer, N. I.; Krein, M., Some Questions in the Theory of Moments (1962), Amer. Math. Soc: Amer. Math. Soc Providence, Rhode Island
[2] Bartels, R.; Golub, G. H., Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations, Comm. A. C. M., 11, 401-406 (1968) · Zbl 0162.20701
[3] Dantzig, G. B., Linear Programming and Extensions (1963), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J · Zbl 0108.33103
[4] D. Galant; D. Galant
[5] Golub, G. H.; Welsch, J., Calculation of Gauss quadrature rules, Math. Comp., 23, 221-230 (1969) · Zbl 0179.21901
[6] Householder, A. S., The Theory of Matrices in Numerical Analysis (1964), Blaisdell: Blaisdell Walthram, Mass · Zbl 0161.12101
[7] Karlin, S.; Studden, W. J., Tchebysheff Systems: With Application in Analysis and Statistics (1966), Interscience Publishers: Interscience Publishers New York · Zbl 0153.38902
[8] Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, Sect. B, 45, 255-282 (1950)
[9] Weinberger, H., A posteriori error bounds in iterative matrix inversion, (Bramble, James H., Symposium on the Numerical Solution of Partial Differential Equations (1966), Academic Press: Academic Press New York/London), 153-163 · Zbl 0146.13405
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