Extreme eigenvalues of real symmetric Toeplitz matrices (Q2701556): Difference between revisions
From MaRDI portal
Set OpenAlex properties. |
Changed label, description and/or aliases in en, and other parts |
||
| label / en | label / en | ||
Extreme | Extreme eigenvalues of real symmetric Toeplitz matrices | ||
| Property / title | |||
| Property / title: Extreme eigenvalues of real symmetric Toeplitz matrices (English) / rank | |||
| Property / title | |||
Extreme eigenvalues of real symmetric Toeplitz matrices (English) | |||
| Property / title: Extreme eigenvalues of real symmetric Toeplitz matrices (English) / rank | |||
Normal rank | |||
| Property / review text | |||
Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others. | |||
| Property / review text: Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others. / rank | |||
Normal rank | |||
| Property / reviewed by | |||
| Property / reviewed by: Erwin O. Kreyszig / rank | |||
Normal rank | |||
Latest revision as of 14:36, 10 April 2025
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extreme eigenvalues of real symmetric Toeplitz matrices |
scientific article |
Statements
19 February 2001
0 references
Toeplitz matrix
0 references
extreme eigenvalues
0 references
odd and even spectra
0 references
spectral equation
0 references
secular equation
0 references
rational approximation
0 references
numerical results
0 references
error analysis
0 references
0 references
0 references
Extreme eigenvalues of real symmetric Toeplitz matrices (English)
0 references
Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others.
0 references
