Summary
We survey computations with general (dense and unstructured) and with dense and structured matrices, including their numerous reductions and correlations to each other and to polynomial computations and their complexity.
The treatment of all these subjects is extensive and complete; the exposition of the algorithms for the computations with dense structured matrices follows the unified and systematic approach based on the study of the associated linear operators.
Furthermore, some recent and unpublished results are included, in particular, new and practically promising algorithms for computation of polynomial gcd and extended Euclidean scheme and for parallel computations with Toeplitz-like and Hankel-like matrices.
The subject of this chapter has substantial impact on other areas of computer science and computational mathematics.
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© 1994 Springer Science+Business Media New York
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Bini, D., Pan, V.Y. (1994). Fundamental Computations with General and Dense Structured Matrices. In: Polynomial and Matrix Computations. Progress in Theoretical Computer Science. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0265-3_2
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DOI: https://doi.org/10.1007/978-1-4612-0265-3_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6686-0
Online ISBN: 978-1-4612-0265-3
eBook Packages: Springer Book Archive