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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.