Minimization of convex functionals over frame operators

被引：21

作者：

Massey, Pedro ^{[1
,2
]}

Ruiz, Mariano ^{[1
]}

机构：

[1] Univ Nacl La Plata, Dept Matemat, La Plata, Buenos Aires, Argentina

[2] IAM CONICET, RA-1083 Buenos Aires, DF, Argentina

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2010年 / 32卷 / 02期

关键词：

Frames; Frame potential; Majorization; TIGHT FRAMES; SEQUENCES;

D O I：

10.1007/s10444-008-9092-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present results about minimization of convex functionals defined over a finite set of vectors in a finite-dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one.

引用

页码：131 / 153

页数：23

共 16 条

[1]

ALBERTI PM, 1981, MATH MONOGRAPHIEN, V18, P123

[2]

Ando T., 1982, MAJORIZATION DOUBLY

[3] The schur-horn theorem for operators and frames with prescribed norms and frame operator [J].

Antezana, J. ;

Massey, P. ;

Ruiz, M. ;

Stojanoff, D. .

ILLINOIS JOURNAL OF MATHEMATICS, 2007, 51 (02) :537-560

[4] Finite normalized tight frames [J].

Benedetto, JJ ;

Fickus, M .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2003, 18 (2-4) :357-385

[5]

Bhatia Rajendra, 1997, Matrix Analysis: Graduate Texts in Mathematics, V169

[6]

Casazza PG, 2006, APPL NUM HARM ANAL, P51

[7] PAINLESS NONORTHOGONAL EXPANSIONS [J].

DAUBECHIES, I ;

GROSSMANN, A ;

MEYER, Y .

JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (05) :1271-1283

[8] A CLASS OF NONHARMONIC FOURIER SERIES [J].

DUFFIN, RJ ;

SCHAEFFER, AC .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAR) :341-366

[9] Convolutional frames and the frame potential [J].

Fickus, M ;

Johnson, BD ;

Kornelson, K ;

Okoudjou, KA .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2005, 19 (01) :77-91

[10]

Horn R.A., 2012, Matrix Analysis

← 1 2 →