Sparsification of Rectangular Matrices
نویسندگان
چکیده
منابع مشابه
Sparsiication of Rectangular Matrices
Given a rectangular matrix with more columns than rows, nd a base of linear combinations of the row vectors such that these contain as many zero entries as possible. This process is called \sparsiication" (of the matrix). A combinatorial search method to solve sparsiication is presented which needs exponentially many arithmetic operations (in terms of the size of the matrix). However, various p...
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Compressed sensing is a relatively new signal processing technique whereby the limits proposed by the Shannon-Nyquist theorem can be exceeded under certain conditions imposed upon the signal. Such conditions occur in many real-world scenarios, and compressed sensing has emerging applications in medical imaging, big data, and statistics. Finding practical matrix constructions and computationally...
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Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of these matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is proposed. Applications are given in (square) eigenvalue computation (Lanczos iteration), square pseudosp...
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We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...
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Given a (k+1)-tuple A,B1, . . . , Bk of (m×n)-matrices withm ≤ n we call the set of all k-tuples of complex numbers {λ1, . . . , λk} such that the linear combination A + λ1B1 + λ2B2 + . . . + λkBk has rank smaller than m the eigenvalue locus of the latter pencil. Motivated primarily by applications to multi-parameter generalizations of the Heine-Stieltjes spectral problem, see [He] and [Vol], w...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1998
ISSN: 0747-7171
DOI: 10.1006/jsco.1998.0204