Convergence of L p -norms of a matrix

Pavel Stavinoha

Aplikace matematiky (1985)

  • Volume: 30, Issue: 5, page 351-360
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Stavinoha, Pavel. "Convergence of $L_p$-norms of a matrix." Aplikace matematiky 30.5 (1985): 351-360. <http://eudml.org/doc/15416>.

@article{Stavinoha1985,
abstract = {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.},
author = {Stavinoha, Pavel},
journal = {Aplikace matematiky},
keywords = {convergence; $L_p$-norms; Hermitian matrix; spectral radius; convergence; -norms; Hermitian matrix; spectral radius},
language = {eng},
number = {5},
pages = {351-360},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of $L_p$-norms of a matrix},
url = {http://eudml.org/doc/15416},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Stavinoha, Pavel
TI - Convergence of $L_p$-norms of a matrix
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 5
SP - 351
EP - 360
AB - 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.
LA - eng
KW - convergence; $L_p$-norms; Hermitian matrix; spectral radius; convergence; -norms; Hermitian matrix; spectral radius
UR - http://eudml.org/doc/15416
ER -

References

top
  1. E. F. Beckenbach, R. Bellman, Inequalities, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1983. (1983) Zbl0513.26003MR0192009
  2. R. Bellman, 10.1016/0362-546X(79)90058-0, Nonlinear Anal. Theory, Meth. and Appl., 3(1979), 905-908. (1979) Zbl0495.65012MR0548962DOI10.1016/0362-546X(79)90058-0
  3. R. T. Gregory, D. L. Karney, A collection of matrices for testing computational algorithms, J. Wiley & Sons., New York, 1969. (1969) MR0253538
  4. L. Gross, 10.1016/0022-1236(72)90057-2, J. Functional Analysis, 10 (1972) 52-109. (1972) Zbl0237.47012MR0339722DOI10.1016/0022-1236(72)90057-2
  5. R. A. Kunze., L p Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc., 89 (1958), 519-540. (1958) MR0100235
  6. J. Peetre, G. Sparr, 10.1007/BF02417016, Ann. of Math. Рurа Appl., 104 (1975), 187-207. (1975) Zbl0309.46031MR0473869DOI10.1007/BF02417016
  7. I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math., 57 (1953), 401-457, correction 58 (1953), 595-596. (1953) Zbl0051.34202MR0054864
  8. P. Stavinoha, On limits of L p -norms of linear operators, Czechoslovak Math. J. 32 (1982), 474-480. (1982) Zbl0511.46062MR0669788

NotesEmbed ?

top

You must be logged in to post comments.