Showing papers on "Matrix decomposition published in 1979"
TL;DR: The factorizedS-matrix with internal symmetry Z4 is constructed in two space-time dimensions and the two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations as mentioned in this paper.
Abstract: The factorizedS-matrix with internal symmetryZ4 is constructed in two space-time dimensions. The two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations. The solution of factorization equations can be expressed in terms of elliptic functions. TheS-matrix contains the resonance poles naturally. The simple formal relation between the general factorizedS-matrices and the Baxter-type lattice transfer matrices is found. In the sense of this relation theZ4-symmetricS-matrix corresponds to the Baxter transfer matrix itself.
135 citations
TL;DR: It is concluded that GPS is exceptionally fast, and, for the conditions under which the test was made, the algorithm best able to reduce profile and rms wavefront consistently well.
Abstract: Three widely-used nodal resequencing algorithms were tested and compared for their ability to reduce matrix profile and root-mean-square (rms) wavefront, the latter being the most critical parameter in determining matrix decomposition time in the NASTRAN finite element computer program. The three algorithms are Cuthill–McKee (CM), Gibbs–Poole–Stockmeyer (GPS), and Levy. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast, and, for the conditions under which the test was made, the algorithm best able to reduce profile and rms wavefront consistently well. An extensive bibliography of resequencing algorithms is included.
91 citations
71 citations
01 Jan 1979
66 citations
TL;DR: In this paper, the authors studied the congruence relation between nonsingular symmetric and skew-symmetric matrices in the set of all real matrices A,B and showed that A and B are S-congruent if there is a nonsingul upper triangular matrix R such that A = RTBR.
42 citations
29 Oct 1979
TL;DR: The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension and trilinear aggregating, uniting and canceling and a fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived.
Abstract: The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schonhage's Theorem about partial and total MM, our approach gives the exponent 2.6054 by the price of a serious increase of the constant.
41 citations
TL;DR: A package of FOTRAN IV subroutines for the out-of-core assembly and solution of a system of linear equations with a non-symmetric coefficient matrix, as met in many finite element applications.
32 citations
TL;DR: In this article, a new algorithm is presented which has computational advantages over existing techniques of solving the minimal design problem, which is illustrated with a physical multivariable example, and the procedure is illustrated using a multiview example.
Abstract: In the past few years several techniqnes for solving the minimal design problem have appeared in the literature. In this paper, a new algorithm is presented which has computational advantages over existing techniques of solving the minimal design problem. The procedure is illustrated with a physical multivariable example.
18 citations
TL;DR: This paper presents a fast iterative algorithm for the solution of a finite difference approximation of the biharmonic boundary value problem on a rectangular region and the matrix decomposition algorithm is efficiently applied to the semi-direct method.
Abstract: This paper presents a fast iterative algorithm for the solution of a finite difference approximation of the biharmonic boundary value problem on a rectangular region. For solving this problem, the matrix decomposition algorithm is efficiently applied to the semi-direct method which essentially treats the biharmonic equation as a coupled system of Poisson equations. Assuming anN×N grid of mesh points, the number of operations required for one iteration and for the solution terminated by 0 (N
−2) is 0 (N
2) and 0 (N
5/2 log2
N), respectively. ForN
2 processors, the parallel version of this algorithm would require 14 log2
N steps per iteration. Both results are better than those known. A numerical experiment in a serial computation is also given.
15 citations
TL;DR: In this paper, the spectral decomposition of the solution operator is applied to nonlinear problems of heat and mass transfer, which can be applied readily to linear transient heat transfer analysis.
TL;DR: A discussion of linear prediction analysis methods that employ the Cholesky decomposition is given and an efficient computational algorithm based on Choleski factorization is derived.
Abstract: A discussion of linear prediction analysis methods that employ the Cholesky decomposition is given. Only one method insures stability of the synthesis filters by assuring that estimated reflection coefficients are bounded in magnitude by one. This estimate is generalized to one based on forward and backward prediction errors. An efficient computational algorithm based on Cholesky factorization is derived.
01 Dec 1979
TL;DR: In this article, the state transition matrix of a linear time-varying system cannot be expressed in a closed form and has, in general, to be evaluated numerically.
Abstract: The state transition matrix of a linear time-varying system cannot, in general, be expressed in a closed form and has, therefore, to be evaluated numerically. For the commutative class of linear time-varying systems, the state-transition matrix is the exponential matrix. A numerical procedure is developed for the evaluation of this matrix to any desired degree of accuracy by the method of series expansion. For linear time-varying systems, which are not restricted to belonging to the commutative class, an efficient computational algorithm is developed for the evaluation of the state-transition matrix. This is based on the minimum m.s.e. approximation of a time function in terms of a set of block-pulse functions, which are orthogonal in the speficied interval. The algorithms developed in the paper are illustrated by appropriate examples.
TL;DR: The model has the distinct advantage of eliminating the problem of combinatorial complexity from problems of calculating optimal information structures and has the advantage that the variable precision of the information read, or equivalently, the variance of the cormpting noise, captures an aspect of organizational form-varying degrees of coordination-not captured by discrete choices of information structures.
Abstract: PlZ=P21=0 bh > q2. preliminary work on cases more complicated than those considered here indicate similar threshold effects in demand for information obtained in more complex situations. However, the complexity of the solution for the inner optimization problem-the general linearquadratic-Gaussian problem in (1.7)-m&es optimization of the information structure and interpretation of the results difficult. The model does have the distinct advantage of eliminating the problem of combinatorial complexity from problems of calculating optimal information structures. It also has the advantage that the variable precision of the information read or equivalently, the variance of the cormpting noise, captures an aspect of organizational form-varying degrees of coordination-not captured by discrete choices of information structures.
TL;DR: Two alternative systematic algorithms are suggested to compute the matrix T necessary to design a minimum-time linear function observer and the simplicity of these algorithms gives mole insight to the understanding of the observer structure.
Abstract: Two alternative systematic algorithms are suggested to compute the matrix T necessary to design a minimum-time linear function observer. The simplicity of these algorithms gives mole insight to the understanding of the observer structure. Furthermore, the computational effort required to obtain the matrix J is spared.
01 Jan 1979
TL;DR: In this article, the authors review the factorization theory for real matrix functions with respect to real divisors and show that the structure of the stable real minimal factorizations is somewhat more complicated than in the complex case.
Abstract: In this chapter we review the factorization theory for the case of real matrix functions with respect to real divisors. As in the complex case the minimal factorizations are completely determined by the supporting projections of a given realization, but of course in this case one has the additional requirement that all linear transformations must be representable by matrices with real entries. Due to the difference between the real and complex Jordan canonical form the structure of the stable real minimal factorizations is somewhat more complicated than in the complex case. This phenomenon is also reflected by the fact that for real matrices there is a difference between the stable and isolated invariant subspaces.
01 May 1979
TL;DR: Simulation results indicate that the magnetic suspension system can operate satisfactorily under the SAFER control method; and factorization techniques indeed enhance the numerical stability of computations.
Abstract: : This project is concerned with the study of the behavior of a particular stochastic system, the magnetic suspension system, under the application of the Sensitivity Adaptive Feedback with Estimation Redistribution (SAFER) Control Algorithm. Matrix factorization techniques are used in the controller and estimator design for the system. Simulation results indicate that the magnetic suspension system can operate satisfactorily under the SAFER control method; and factorization techniques indeed enhance the numerical stability of computations. However, due to the complex structure of the SAFER control method, real time application of the algorithm may require faster computing device or simplified mathematical model. Its application will be most pertinent to system with slow time constants. (Author)