Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors

  • B. N. Parlett
  • C. Reinsch
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


This algorithm is based on the work of Osborne [1]. 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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    Osborne, E. E.: On pre-conditioning of matrices. J. Assoc. Comput. Mach. 7, 338–345 (i960).MathSciNetMATHCrossRefGoogle Scholar
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© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • B. N. Parlett
  • C. Reinsch

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