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Separable Type Representations of Matrices and Fast Algorithms: Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms (Operator Theory: Advances and Applications)

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This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike.?
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Introduction to Probability and Statistics Using R
Introduction to Probability and Statistics Using R
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Algorithms in Invariant Theory (Texts & Monographs in Symbolic Computation)
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An Introduction to R
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The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations

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Applied Data Mining
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Data mining has witnessed substantial advances in recent decades. New research questions and practical challenges have arisen from emerging areas and applications within the various fields closely related to human daily life, e.g. social media and social networking. This book aims to bridge the gap between traditional data mining and...

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