Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem. (Q1414695)

The authors define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem (MEP) \((V_{i0}-\sum _{j=1}^k \lambda _j V_{ij})x_i =0 \neq x_i , \quad i=1,\dots ,k,\) \noindent where the \(V_{ij}\) are \(n_i \times n_i\) complex matrices. They define and characterize the pseudospectrum for the MEP and show that the distance from a right definite MEP to the closest non right definite MEP is related to the smallest unbounded pseudospectrum.