矩阵的非线性谱与极值问题

USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 DOI:10.1016/0041-5553(90)90199-3

A.N. Buslayev

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引用次数: 0

摘要

寻找系统Aτ(Ax)(q) = λq(x)(p)的谱值λ和向量xϵRm{ϵ0}的理论问题和计算方面，其中a是k × m矩阵，1≤p, q <∞呈现。非线性系统((p−2)2 + (q−2)2≠0)在分析、力学和近似理论的许多领域中都有出现。

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Non-linear spectra of matrices and extremal problems

Theoretical questions and the computational aspects of the search for the spectral values λ and vectors xϵR^m{ϵ0} of a system A^τ(Ax)_(q) = λ^q(x)_(p), where A is a k × m matrix, 1 ⩽ p, q < ∞ are presented. When p = q = 2 this is simply the problem of determining the singular values of A. Nonlinear systems ((p − 2)² + (q − 2)² ≠ 0) arise in many fields of analysis, mechanics and approximation theory.

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USSR Computational Mathematics and Mathematical Physics

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