| Title:
|
Convergence of $L_p$-norms of a matrix (English) |
| Author:
|
Stavinoha, Pavel |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
30 |
| Issue:
|
5 |
| Year:
|
1985 |
| Pages:
|
351-360 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
a recurrence relation for computing the $L_p$-norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the $L_p$-norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed. (English) |
| Keyword:
|
convergence |
| Keyword:
|
$L_p$-norms |
| Keyword:
|
Hermitian matrix |
| Keyword:
|
spectral radius |
| MSC:
|
15A12 |
| MSC:
|
15A42 |
| MSC:
|
15A60 |
| MSC:
|
65F15 |
| MSC:
|
65F35 |
| idZBL:
|
Zbl 0609.65024 |
| idMR:
|
MR0806832 |
| DOI:
|
10.21136/AM.1985.104162 |
| . |
| Date available:
|
2008-05-20T18:28:19Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104162 |
| . |
| Reference:
|
[1] E. F. Beckenbach, R. Bellman: Inequalities.Springer-Verlag, Berlin Heidelberg New York Tokyo, 1983. Zbl 0513.26003, MR 0192009 |
| Reference:
|
[2] R. Bellman: Selective computation - V: The largest characteristic root of a matrix.Nonlinear Anal. Theory, Meth. and Appl., 3(1979), 905-908. Zbl 0495.65012, MR 0548962, 10.1016/0362-546X(79)90058-0 |
| Reference:
|
[3] R. T. Gregory, D. L. Karney: A collection of matrices for testing computational algorithms.J. Wiley & Sons., New York, 1969. MR 0253538 |
| Reference:
|
[4] L. Gross: Existence and uniqueness of physical ground states.J. Functional Analysis, 10 (1972) 52-109. Zbl 0237.47012, MR 0339722, 10.1016/0022-1236(72)90057-2 |
| Reference:
|
[5] R. A. Kunze. : $L_p$ Fourier transforms on locally compact unimodular groups.Trans. Amer. Math. Soc., 89 (1958), 519-540. MR 0100235 |
| Reference:
|
[6] J. Peetre, G. Sparr: Interpolation and non-commutative integration.Ann. of Math. Рurа Appl., 104 (1975), 187-207. Zbl 0309.46031, MR 0473869, 10.1007/BF02417016 |
| Reference:
|
[7] I. E. Segal: A non-commutative extension of abstract integration.Ann. of Math., 57 (1953), 401-457, correction 58 (1953), 595-596. Zbl 0051.34202, MR 0054864 |
| Reference:
|
[8] P. Stavinoha: On limits of $L_p$-norms of linear operators.Czechoslovak Math. J. 32 (1982), 474-480. Zbl 0511.46062, MR 0669788 |
| . |
