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A QR Decomposition for Matrix Pencils
BIT Numerical Mathematics, 2000An efficient and numerically stable modification of the \(QR\) decomposition for solving a linear least squares problem with a matrix of the form \(A+\lambda B\) is given. The idea is to proceed by columns and in step \(i\) the algorithm is driven by data from column \(i\) of the transformed matrices \(B\) and \(A\) in turn.
W. M. Hartmann, Peter Spellucci
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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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Cholesky decomposition of the Hilbert matrix
Japan Journal of Applied Mathematics, 1988The paper deals with a modified Cholesky decomposition \(H=LDL\) T, of the Hilbert matrix \(H=[1/(j+k-1)],\) where L is lower triangular with diagonal elements being 1, D is diagonal, L T is the transpose of L. Precise formulas for the Cholesky components L, D and the inverse \(L^{-1}\) are given.
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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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Auto-weighted multi-view clustering via deep matrix decomposition
Pattern Recognition, 2020Shudong Huang, Zhao Kang, Zenglin Xu
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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