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Research supported by the National Natural Science Foundation of China (Grant No. 11471279), the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2017JJ1025) and the Research Foundation of Education Bureau of Hunan Province (Grant No. 14B178).
In this paper, we consider the product eigenvalue problem for a wide class of structured matrices containing the well-known Vandermonde and Cauchy matrices. A periodic qd-type reduction method is developed for computing eigenvalues of products of these rectangular matrices so that no subtraction of like-signed numbers occurs. Consequently, all the eigenvalues of such a product are computed to high relative accuracy in a preferable complexity. Error analysis and numerical experiments are provided to confirm the high relative accuracy.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge (2007) MATH
Watkins, D.S.: The Matrix Eigenvalue Problem: GR and KrylovSubsp ace Methods. SIAM, Philadelphia (2007) CrossRef
- A Periodic qd-Type Reduction for Computing Eigenvalues of Structured Matrix Products to High Relative Accuracy
- Publication date
- Springer US
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