Differential analysis of matrix convex functions

Research output: Contribution to journal › Journal article › Research › peer-review

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Differential analysis of matrix convex functions. / Hansen, Frank; Tomiyama, Jun.

In: Linear Algebra and Its Applications, Vol. 420, No. 1, 2007, p. 102-116.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Hansen, F & Tomiyama, J 2007, 'Differential analysis of matrix convex functions', Linear Algebra and Its Applications, vol. 420, no. 1, pp. 102-116. https://doi.org/10.1016/j.laa.2006.06.018

APA

Hansen, F., & Tomiyama, J. (2007). Differential analysis of matrix convex functions. Linear Algebra and Its Applications, 420(1), 102-116. https://doi.org/10.1016/j.laa.2006.06.018

Vancouver

Hansen F, Tomiyama J. Differential analysis of matrix convex functions. Linear Algebra and Its Applications. 2007;420(1):102-116. https://doi.org/10.1016/j.laa.2006.06.018

Author

Hansen, Frank ; Tomiyama, Jun. / Differential analysis of matrix convex functions. In: Linear Algebra and Its Applications. 2007 ; Vol. 420, No. 1. pp. 102-116.

Bibtex

@article{fe5fbee0bdcb11dbbee902004c4f4f50,
title = "Differential analysis of matrix convex functions",
abstract = "We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, {\"U}ber konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for matrix convexity which are necessary and locally sufficient, and they allow us to prove the existence of gaps between classes of matrix convex functions of successive orders, and to give explicit examples of the type of functions contained in each of these gaps. The given conditions are shown to be also globally sufficient for matrix convexity of order two. We finally introduce a fractional transformation which connects the set of matrix monotone functions of each order n with the set of matrix convex functions of the following order n + 1",
keywords = "Faculty of Social Sciences, matrix convex function, polynomial",
author = "Frank Hansen and Jun Tomiyama",
note = "JEL classification: C02",
year = "2007",
doi = "10.1016/j.laa.2006.06.018",
language = "English",
volume = "420",
pages = "102--116",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Differential analysis of matrix convex functions

AU - Hansen, Frank

AU - Tomiyama, Jun

N1 - JEL classification: C02

PY - 2007

Y1 - 2007

N2 - We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for matrix convexity which are necessary and locally sufficient, and they allow us to prove the existence of gaps between classes of matrix convex functions of successive orders, and to give explicit examples of the type of functions contained in each of these gaps. The given conditions are shown to be also globally sufficient for matrix convexity of order two. We finally introduce a fractional transformation which connects the set of matrix monotone functions of each order n with the set of matrix convex functions of the following order n + 1

AB - We analyze matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [F. Kraus, Über konvekse Matrixfunktionen, Math. Z. 41 (1936) 18-42]. We obtain for each order conditions for matrix convexity which are necessary and locally sufficient, and they allow us to prove the existence of gaps between classes of matrix convex functions of successive orders, and to give explicit examples of the type of functions contained in each of these gaps. The given conditions are shown to be also globally sufficient for matrix convexity of order two. We finally introduce a fractional transformation which connects the set of matrix monotone functions of each order n with the set of matrix convex functions of the following order n + 1

KW - Faculty of Social Sciences

KW - matrix convex function

KW - polynomial

U2 - 10.1016/j.laa.2006.06.018

DO - 10.1016/j.laa.2006.06.018

M3 - Journal article

VL - 420

SP - 102

EP - 116

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1

ER -

ID: 340183