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Sparse Matrix-Matrix Products Executed Through Coloring
SIAM Journal on Matrix Analysis and Applications, 2015Summary: Sparse matrix-matrix products appear in multigrid solvers among other applications. Some implementations of these products require the inner product of two sparse vectors. In this paper, we propose a new algorithm for computing sparse matrix-matrix products by exploiting their nonzero structure through the process of graph coloring.
McCourt, Michael +2 more
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Linear and Multilinear Algebra, 1975
Let Σ(F) be the class of hermitian positive definite elements of Mn (F), where F is either R, the real, or C, the complex field, and let For j ⩾ 0 and k ⩾ 1, all set products of the form: are determined for integers j k. This completes earlier work of Ballantine and Taussky which determined for integers j ⩾ 0.
C.S. Ballantine, C.R. Johnson
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Let Σ(F) be the class of hermitian positive definite elements of Mn (F), where F is either R, the real, or C, the complex field, and let For j ⩾ 0 and k ⩾ 1, all set products of the form: are determined for integers j k. This completes earlier work of Ballantine and Taussky which determined for integers j ⩾ 0.
C.S. Ballantine, C.R. Johnson
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“Random” random matrix products
Journal d'Analyse Mathématique, 2001This paper studies compositions of independent random bundle maps \(F(x,a)=f_Fx,T_F(x)a\), \(x\in X\), \(a\in \mathbb R^d\), where \(X\) is a Borel subset of a Polish space, whose distributions form a stationary process. This specializes to the case of products of independent random matrices evolving by a stationary process and generalizes many results
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1987
Turning back to the correlation matrix Σ = (σαβ) associated, in the previous chapter, with the primitive and aperiodic substitution ζ of length q, we shall prove that Σ is the weak-star limit point of a product of matrices whose entries are trigonometric polynomials, in a way similar to the case of generalized Riesz products.
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Turning back to the correlation matrix Σ = (σαβ) associated, in the previous chapter, with the primitive and aperiodic substitution ζ of length q, we shall prove that Σ is the weak-star limit point of a product of matrices whose entries are trigonometric polynomials, in a way similar to the case of generalized Riesz products.
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Computing roots of matrix products
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2001AbstractThe problem of computing a kth root of a matrix product W = Πki=1 Ai is considered. The explicit computation of W may produce a highly inaccurate result due to rounding errors, such that the computed root W1/k is far from the actual root W1/k. An algorithm for computing the square root of W is presented which avoids the explicit computation of ...
Benner, P. ; https://orcid.org/0000-0003-3362-4103 +1 more
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A CCD matrix matrix product parallel processor
1984 IEEE International Solid-State Circuits Conference. Digest of Technical Papers, 1984The design of a CCD matrix-matrix device operating up to 10MHz clock rates, performing the serial-in parallel-out and Fourier transform functions required in radar doppler filtering, will be reported. The chip contains 32 multipliers and 1024 accumulators.
A. Chiang +3 more
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The Global Productivity Matrix:
Journal of Global Marketing, 1992Global sales force allocation decisions are among the most important and most difficult decisions facing the multinational enterprise. While much has been written about sales force deployment in general, the literature is void of specific deployment approaches for the global sales force.
Joel Herche, Michael J Swenson
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2012
The term ‘matrix-product state’ (MPS) is introduced in quantum physics (see, e.g., Verstraete-Cirac [190], [105, Eq. (2)]). The related tensor representation can be found already in Vidal [191] without a special naming of the representation. The method has been reinvented by Oseledets and Tyrtyshnikov ([152], [155], [159]) and called ‘TT decomposition’.
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The term ‘matrix-product state’ (MPS) is introduced in quantum physics (see, e.g., Verstraete-Cirac [190], [105, Eq. (2)]). The related tensor representation can be found already in Vidal [191] without a special naming of the representation. The method has been reinvented by Oseledets and Tyrtyshnikov ([152], [155], [159]) and called ‘TT decomposition’.
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Matrix-product neural network based on sequence block matrix product
The Journal of Supercomputing, 2022Chuanhui Shan, Jun Ou, Xiumei Chen
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