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Application of Matrix Decompositions for Matrix Canonization
Computational Mathematics and Mathematical Physics, 2019© 2019, Pleiades Publishing, Ltd. Abstract: The problem of solving overdetermined, underdetermined, singular, or ill conditioned SLAEs using matrix canonization is considered. A modification of an existing canonization algorithm based on matrix decomposition is proposed.
Volkov V., Dem’yanov D.
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On the cartesian decomposition of a matrix
Linear and Multilinear Algebra, 1985The main result of this paper is the following Let A and B be n×n hermitian matrices with eigenvalues respectively, ordered so that and let M1 be any k×k principal submatrix of . Necessary and sufficient conditions for equality are given.
António Leal Duarte +1 more
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Decomposition of a symmetric matrix
Numerische Mathematik, 1976An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for solving associated systems of linear equations are included.
Linda Kaufman +2 more
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A decomposition for in-place matrix transposition [PDF]
Proceedings of the 19th ACM SIGPLAN symposium on Principles and practice of parallel programming, 2014 We describe a decomposition for in-place matrix transposition, with applications to Array of Structures memory accesses on SIMD processors. Traditional approaches to in-place matrix transposition involve cycle following, which is difficult to parallelize, and on matrices of dimension m by n require O(mn log mn) work when limited to less than O(mn ...
KellerAlexander +2 more
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Matrix decomposition MFS algorithms [PDF]
WIT Transactions on Modelling and Simulation, Vol 42, 2006 The Method of Fundamental Solutions (MFS) is a boundary–type meshless method for the solution of certain elliptic boundary value problems. We exploit the symmetries of the matrices appearing when this method is applied to certain three-dimensional elliptic problems and develop an efficient algorithm for their solution.
Karageorghis, Andreas +3 more
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Freeness and matrix decompositions
Science China Mathematics, 2011If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra (with respect to a normal trace), then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of (joint) distribution.
Junhao Shen, Liming Ge, Liming Ge
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N-decomposition and decomposition matrix for automata
Proceedings of the annual conference on - ACM'73, 1973This continues the study on generalized mutiple decomposition allowing 2-way interconnection [1]. Let NeZ+.An automaton M e D, T,F> is an N-automaton iff the set of states D ≤ πSi and each Si e πi (D) where πi is the projection map onto the ith component.
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On ANOVA-Like Matrix Decompositions [PDF]
, 2015 The analysis of variance plays a fundamental role in statistical theory and practice, the standard Euclidean geometric form being particularly well established. The geometry and associated linear algebra underlying such standard analysis of variance methods permit, essentially direct, generalisation to other settings. Specifically, as jointly developed
BOVE, Giuseppe +3 more
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1985
Let a matrix game be given by the hypermatrix $${\text{A = }}\left[ {\begin{array}{*{20}{l}}{{{\text{A}}_{11}}}&{{{\text{A}}_{12}}}& \cdots &{{{\text{A}}_{{\text{1}}N}}} \\ {{{\text{A}}_{21}}}&{{{\text{A}}_{22}}}& \cdots &{{{\text{A}}_{2N}}} \\ \cdots & \cdots & \cdots & \cdots \\ {{{\text{A}}_{M1}}}&{{{\text{A}}_{M2}}}& \cdots &{{{\text{A}}_{MN}}}
F. Forgó, J. Szép
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Let a matrix game be given by the hypermatrix $${\text{A = }}\left[ {\begin{array}{*{20}{l}}{{{\text{A}}_{11}}}&{{{\text{A}}_{12}}}& \cdots &{{{\text{A}}_{{\text{1}}N}}} \\ {{{\text{A}}_{21}}}&{{{\text{A}}_{22}}}& \cdots &{{{\text{A}}_{2N}}} \\ \cdots & \cdots & \cdots & \cdots \\ {{{\text{A}}_{M1}}}&{{{\text{A}}_{M2}}}& \cdots &{{{\text{A}}_{MN}}}
F. Forgó, J. Szép
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Matrix and Tensor Decompositions
2010Advances in high-throughput technologies such as gene and protein expression microarrays in the past decade have made it possible to simultaneously measure the expression levels of thousands of transcripts. This has resulted in large amounts of biological data requiring analysis and interpretation.
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