Non-linear spectra of matrices and extremal problems

A. P. Buslaev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 6, pp. 803-816

Résumé

Theoretical questions and the computational aspects of the search for the spectral values $\lambda$ and vectors $x\in\mathbb R^m\setminus\{0\}$ of a system $A^{\mathrm T}(Ax)_{(q)}=\lambda^q(x)_{(p)}$, where $A$ is a $k\times m$ matrix, $1\le p$, $q\infty$ are presented. When $p=q=2$ this is simply the problem of determining the singular values of $A$. Nonlinear systems $((p-2)^2+(q-2)^2\ne0)$ arise in many fields of analysis, mechanics and approximation theory.