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Application of Matrix Decompositions for Matrix Canonization
Computational Mathematics and Mathematical Physics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Volkov V., Dem’yanov D.
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Matrix Algebras and Displacement Decompositions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2000 This paper investigates classes of complex \(n\times n\) matrices for which there are formulae enabling computation of a matrix vector product \(Af\) by means of a small number of fast discrete transforms. The basic formula is the ``displacement formula'': \(A=\sum_{m=1}^{\alpha}L_{m}U_{m}\) where \(L_{m}\) and \(U_{m}\) are lower and upper triangular ...
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On Huynen's Decomposition of a Kennaugh Matrix
IEEE Geoscience and Remote Sensing Letters, 2006For some special case, Huynen's decomposition cannot be used to extract a desired target from an average Kennaugh matrix. In this paper, the authors modify Huynen's method for overcoming its disadvantage, based on a simple transform of a Kennaugh matrix.
Jian Yang, Ying-Ning Peng
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On LU decomposition of a centrosymmetric matrix
Information Sciences, 1992An \(LU\) decomposition of a centrosymmetric matrix, the Choleski decomposition of a centrosymmetric, symmetric and positively defined matrix, as well as algorithms for finding the inverse of such a matrix by using this decomposition are presented in the paper.
Ivatury Ramabhadrasarma +2 more
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Accelerating matrix decomposition with replications
2008 IEEE International Symposium on Parallel and Distributed Processing, 2008Matrix decomposition applications that involve large matrix operations can take advantage of the flexibility and adaptability of reconfigurable computing systems to improve performance. The benefits come from replication, which includes vertical replication and horizontal replication.
Yi-Gang Tai +2 more
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Matrix decomposition on the star graph
IEEE Transactions on Parallel and Distributed Systems, 1997We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N/sup 3//n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N/spl ges/(n-1)!.
Abdel Elah Al-Ayyoub, Khaled Day
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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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Fast Polar Decomposition of an Arbitrary Matrix [PDF]
SIAM Journal on Scientific and Statistical Computing, 1990 The polar decomposition of an $m \times n$ matrix A of full rank, where $m \geqq n$, can be computed using a quadratically convergent algorithm of Higham [SIAM J. Sci. Statist. Comput., 7(1986), pp. 1160–1174]. The algorithm is based on a Newton iteration involving a matrix inverse.
Nicholas J Higham
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Matrix decomposition and data reduction
Computers & Graphics, 1995Abstract In this paper, we present a class of decomposition techniques for data represented as matrices. The main idea is to transform a matrix into a sequence of components in order to represent and analyze the matrix in a multi-resolution setting. Data reduction is obtained by maintaining only entries of each matrix component that give significant ...
Morten Dæhlen, Per Gunnar Holm
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Interpretable nonnegative matrix decompositions
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, 2008A matrix decomposition expresses a matrix as a product of at least two factor matrices. Equivalently, it expresses each column of the input matrix as a linear combination of the columns in the first factor matrix. The interpretability of the decompositions is a key issue in many data-analysis tasks. We propose two new matrix-decomposition problems: the
Saara Hyvönen +2 more
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