Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors
This algorithm is based on the work of Osborne . He pointed out that existing eigenvalue programs usually produce results with errors at least of order ε‖A‖ E , where is the machine precision and ‖A‖ E is the Euclidean (Frobenius) norm of the given matrix A**. Hence he recommends that one precede the calling of such a routine by certain diagonal similarity transformations of A designed to reduce its norm.
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