论文信息 - The construction of Jacobi and periodic Jacobi matrices with prescribed spectra

The construction of Jacobi and periodic Jacobi matrices with prescribed spectra

Abstract : The spectral properties of Jacobi and periodic Jacobi matrices are analyzed and algorithms for the construction of Jacobi and periodic Jacobi matrices with prescribed spectra are presented. Numerical evidence demonstrates that these algorithms are of practical utility. These algorithms have been used in studies of the periodic Toda lattice, and might also be used in studies of inverse eigenvalue problems for Sturm-Louiville equations and Hill's equation. (Author)

Warren E. Ferguson | W. Ferguson

[1] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[2] F. R. Gantmakher,et al. Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme , 1960 .

[3] Polynomial approximations to finitely oscillating functions , 1961 .

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

[5] Alston S. Householder,et al. Handbook for Automatic Computation , 1960, Comput. J..

[6] G. Stewart. Introduction to matrix computations , 1973 .

[7] Gene H. Golub,et al. Eigenproblems for matrices associated with periodic boundary conditions. , 1975 .

[8] P. Moerbeke,et al. The spectrum of Jacobi matrices , 1976 .

[9] D. McLaughlin,et al. Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions*) , 1976 .

[10] Ole H. Hald,et al. Inverse eigenvalue problems for Jacobi matrices , 1976 .

[11] Gene H. Golub,et al. Inverse eigenvalue problems for band matrices , 1978 .