A new algorithm is presented for the efficient solution of large least squares problems in which the coefficient matrix of the linear system is a Kronecker product of two smaller dimension matrices. The solution algor...
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A new algorithm is presented for the efficient solution of large least squares problems in which the coefficient matrix of the linear system is a Kronecker product of two smaller dimension matrices. The solution algorithm is based on QR factorizations of the smaller dimension matrices. Near perfect load balancing is achieved by exploiting a 'commutativity' property of the Kronecker product, and communication requirements are minimized by employing a binary exchange algorithm for matrix transposition. The parallel algorithm is presented, and timing results are shown from test runs on an Intel i860 computer.
We use the Euler, Jacobi, Poincare, and Brun matrix algorithms as well as two new algorithms to evaluate the continued fraction expansions of two vectors L related to two Davenport cubic forms g(1) and g(2). The Klein...
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We use the Euler, Jacobi, Poincare, and Brun matrix algorithms as well as two new algorithms to evaluate the continued fraction expansions of two vectors L related to two Davenport cubic forms g(1) and g(2). The Klein polyhedra of g(1) and g(2) were calculated in another paper. Here the integer convergents P-k given by the cited algorithms are considered with respect to the Klein polyhedra. We also study the periods of these expansions. It turns out that only the Jacobi and Bryuno algorithms can be regarded as satisfactory.
In the present paper is presented a numerical method for the exact reduction of a singlevariable polynomial matrix to its Smith form without finding roots and without applying unimodular transformations. Using the not...
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The general problem considered here is the least squares solution of(A x B)x = t, where A and B are full rank, rectangular matrices, and A x B is the Kronecker product of A and B. Equations of this form arise in areas...
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The general problem considered here is the least squares solution of(A x B)x = t, where A and B are full rank, rectangular matrices, and A x B is the Kronecker product of A and B. Equations of this form arise in areas such as digital image and signal processing, photogrammetry, finite elements, and multidimensional approximation. An efficient method of solution is based on QR factorizations of the original matrices A and B. It is demonstrated how these factorizations can be used to obtain the Cholesky factorization of the least squares coefficient matrix without explicitly forming the normal equations. A similar approach based on singular value decomposition (SVD) factorizations also is indicated for the rank-deficient case. Key words. Kronecker product, overdetermined least squares, QR factorization, SVD factorization, matrix algorithms
Discusses matrix computations using Fortran computer program language and paging. Influence of the order of nested loops on the efficiency of conventional Fortran programs; Effect of nested loop modifications on large...
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Discusses matrix computations using Fortran computer program language and paging. Influence of the order of nested loops on the efficiency of conventional Fortran programs; Effect of nested loop modifications on large programs run under paging-based operating system.
matrix representations and operations are examined for the purpose of minimizing the page faulting occurring in a paged memory system. It is shown that carefully designed matrix algorithms can lead to enormous savings...
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matrix representations and operations are examined for the purpose of minimizing the page faulting occurring in a paged memory system. It is shown that carefully designed matrix algorithms can lead to enormous savings in the number of page faults occurring when only a small part of the total matrix can be in main memory at one time. Examination of addition, multiplication, and inversion algorithms shows that a partitioned matrix representation (i.e. one submatrix or partition per page) in most cases induced fewer page faults than a row-by-row representation. The number of page-pulls required by these matrix manipulation algorithms is also studied as a function of the number of pages of main memory available to the algorithm. [ABSTRACT FROM AUTHOR]
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