论文信息 - Estimates of Eigenvalues for Iterative Methods

Estimates of Eigenvalues for Iterative Methods

We describe a procedure for determining estimates of the eigenvalues of operators used in various iterative methods for the solution of linear systems of equations. We also show how to determine upper and lower bounds for the error in the approximate solution of linear equations, using essentially the same information as that needed for the eigenvalue calculations. The methods described depend strongly upon the theory of moments and Gauss quadrature.

G. Golub | M. D. Kent

[1] C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators , 1950 .

[2] R. Varga,et al. Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods , 1961 .

[3] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[4] R. A. Sack,et al. An algorithm for Gaussian quadrature given modified moments , 1971 .

[5] G. Golub,et al. Bounds for the error of linear systems of equations using the theory of moments , 1972 .

[6] J. Wheeler,et al. Modified moments and Gaussian quadratures , 1974 .

[7] W. Gautschi. Questions of Numerical Condition Related to Polynomials , 1978 .

[8] G. Golub,et al. Bounds for the error in linear systems , 1979 .

[9] W. Gautschi. On Generating Orthogonal Polynomials , 1982 .