文章基本信息

标题：Eigenvalue And Singular Value Optimization
本地全文：下载
作者：Anibal M. Blanco ; J. Alberto Bandoni
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2007
页码：1258-1272
语种：English
出版社：CIMEC-INTEC-CONICET-UNL
摘要：Eigenvalues, singular values and condition number of matrices, play an important role in many fields of applied mathematics to engineering. Among the plethora of applications of eigenvalues in mathematics and engineering we can mention numerical analysis, structural design, quantum mechanics and system dynamics (physical and biological models). For some applications it may be desirable to choose the parameters of a model in order to optimize an objective function and/or to verify constraints that involve eigenvalues or singular values of a certain matrix. In general, the elements of the matrix depend in a nonlinear fashion on the optimization parameters. The purpose of this contribution is to introduce recent formulations of eigenvalue and singular value optimization as well as techniques to include condition numbers within the optimization problem. A chemical engineering design problem is presented to illustrate the proposed techniques.
其他摘要：Eigenvalues, singular values and condition number of matrices, play an important role in many fields of applied mathematics to engineering. Among the plethora of applications of eigenvalues in mathematics and engineering we can mention numerical analysis, structural design, quantum mechanics and system dynamics (physical and biological models). For some applications it may be desirable to choose the parameters of a model in order to optimize an objective function and/or to verify constraints that involve eigenvalues or singular values of a certain matrix. In general, the elements of the matrix depend in a nonlinear fashion on the optimization parameters. The purpose of this contribution is to introduce recent formulations of eigenvalue and singular value optimization as well as techniques to include condition numbers within the optimization problem. A chemical engineering design problem is presented to illustrate the proposed techniques.