By Vadim Olshevsky

The best recognized speedy computational algorithms is the quick Fourier rework technique. Its potency relies in general at the specified constitution of the discrete Fourier remodel matrix. lately, many different algorithms of this kind have been came across, and the speculation of established matrices emerged. This quantity includes 22 survey and study papers dedicated to numerous theoretical and useful points of the layout of quickly algorithms for dependent matrices and similar concerns. integrated during this name are a number of papers containing quite a few affirmative and adverse leads to this path. the idea of rational interpolation is without doubt one of the first-class assets offering instinct and strategies to layout quickly algorithms.The quantity comprises numerous computational and theoretical papers at the subject. There are a number of papers on new functions of based matrices, e.g., to the layout of quick interpreting algorithms, computing state-space realizations, family members to Lie algebras, unconstrained optimization, fixing matrix equations, and so on. The booklet is acceptable for mathematicians, engineers, and numerical analysts who layout, learn, and use quickly computational algorithms in response to the speculation of dependent matrices.

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