Parallel variants of the multishift QZ algorithm with advanced deflation techniques
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
An algorithm for the complete solution of quadratic eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Stability of rootfinding for barycentric Lagrange interpolants
Numerical Algorithms
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We present a new diagonal balancing technique for regular matrix pencils $\lambda B-A$, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired by the balancing technique of a square matrix A and has a comparable complexity. The diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also show that balancing a pencil boils down to making it closer to some standardized normal pencil. We give numerical examples illustrating that the sensitivity of generalized eigenvalues of a pencil may significantly improve after balancing.