BALANCING REGULAR MATRIX PENCILS.

We present a new diagonal balancing technique for regular matrix pencils λB — 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. [ABSTRACT FROM AUTHOR]