Backward Error of Polynomial Eigenproblems Solved by Linearization
Backward Error of Polynomial Eigenproblems Solved by Linearization
The most widely used approach for solving the polynomial eigenvalue problem $P(\lambda)x = (\sum_{i=0}^m \l^i A_i) x = 0$ in $n\times n$ matrices $A_i$ is to linearize to produce a larger order pencil $L(\lambda) = \lambda X + Y$, whose eigensystem is then found by any method for generalized eigenproblems. …