Showing papers on "Matrix difference equation published in 1978"
107 citations
TL;DR: In this paper, conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory.
53 citations
TL;DR: By considering the square root of a matrix as a special case of matrix Riccati-type equations, a fast economical algorithm was developed as a stable generalization of the process given in this paper.
Abstract: By considering the square root of a matrix as being a special case of a matrix Riccati-type equation, a fast economical algorithm is developed as a stable generalization of the process given in [1].
41 citations
TL;DR: In this article, closed form matrix equations are given for the information matrix of the parameters of the vector mixed autoregressive moving average time series model, and closed form equations are also given for information matrix.
28 citations
TL;DR: In this article, the solution to the Riccati equation is given in terms of the partition of the transition matrix and matrix differential equations are derived and solved using methods developed in the fields of free vibration theory and aircraft flutter analysis.
25 citations
23 citations
13 citations
12 citations
TL;DR: In this article, the authors study the solutions X to the quadratic operator equation XBX + XA − DX − C = 0 via the invariant subspace structure of an associated operator matrix.
11 citations
TL;DR: In this paper, a theoretical explanation of the O(h?l) rate of convergence observed in the application of a multiple grid method to a model finite difference Poisson problem is provided.
Abstract: 1. This note provides a theoretical explanation of the O(h?l) rate of convergence observed in the application of a multiple grid method to a model finite difference Poisson problem. The method in question was proposed in [2] and some numerical results were given from which the O(h/2) figure was inferred. This method consists of applying a second degree acceleration technique to the iterates from a linear stationary iterative method of the first degree. Only the latter involves anything new-it is the multiple grid part of the algorithm-and is all that will be considered here. More specifically, once the spectral properties of the iterating matrix of the first degree process are established, the properties of the composite algorithm can be deduced by standard techniques. These were discussed in [2] and well-known books and papers [1], [3], [4] may be consulted for more details. Use of these techniques will be made in Section 4. In Sections 2 and 3 the necessary theoretical preliminaries are developed.
9 citations
TL;DR: In this paper, the sign matrix function algorithm is used to solve the discrete Riccati equation, which arises in the optimisation problem of the discrete regulator with quadratic cost criterion.
Abstract: The sign matrix function algorithm is used to solve the discrete Riccati equation which arises in the optimisation problem of the discrete regulator with quadratic cost criterion.
TL;DR: In this paper, the transition matrix for the Mathieu equation was developed using the general solution of that equation and the coefficients of the phase space ellipse derived from consideration of u max.
TL;DR: In this paper, the classical perturbation method is employed to obtain the solution in the form of a series which is shown to be convergent in transient as well as in the steady-state behaviour of the Riccati equation.
Abstract: This paper is concerned with the solution of a matrix Riccati equation encountered in quadratic minimization problems of optimal and filtering control theory. The classical perturbation method is employed to obtain the solution in the form of a series which is shown to be convergent in transient as well as in the steady-state behaviour of the Riccati equation. An estimate of error which results, due to truncation of the series after a finite number of terms, is also given.
TL;DR: In this article, the CAUCHY-PEXIDER functional equation is generalized to the form H ((xc±yc)1/c) = F(x) G(y), c≠0, assuming the function H (x) possesses a measurable majorant on a set of positive measure.
Abstract: The CAUCHY-PEXIDER functional equation H (x±y)=F(x) G(y) is generalized to the form H ((xc±yc)1/c) = F(x) G(y), c≠0, assuming the function H(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.
TL;DR: In this article, sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval, where the criteria involve integral conditions on the coefficient matrices of the Riemannian equation.
Abstract: Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval The criteria involve integral conditions on the coefficient matrices of the Riccati equation The present results are compared with previously known results
TL;DR: In this paper, an integral equation is found which describes both the initial and kinetic stages of relaxation of the density matrix of a subsystem from any initial distribution, which makes it possible when computing a partially traced density matrix to use the method of two-time quantum Green's functions.
Abstract: A unitary transformation is indicated which makes it possible when computing a partially traced density matrix to use the method of two-time quantum Green's functions. For systems in strong nonequilibrium, an integral equation is found which describes both the initial and kinetic stages of relaxation of the density matrix of a subsystem from any initial distribution.
TL;DR: An initial matrix, based on the parameter imbedded solution of the Riccati equation, is introduced for the Newton's algorithm, which has improved the required CPU time of previous initialization schemes by as much as a factor of 6 times for the same order of accuracy.
TL;DR: This paper proposes a method for determining the state transition matrix by minimizing a given quadratic criterion and shows that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.
TL;DR: A functional equation involving vector mean values is defined in this paper, where the vector mean value is defined as a function of the vector norm of the mean value of a vector vector.
Abstract: of Australasian PhD thesis A functional equation involving vector mean values
TL;DR: In this article, a matrix bilinear delay-differential equation is solved using a new form for the solution of this equation, and controlability results are obtained for a matrix delay differential equation.
Abstract: Controllability results are obtained for a matrix bilinear delay-differential equation. This is achieved by the use of a new form for the solution of this equation.
TL;DR: In this paper, it is shown that by using a proper transformation on the state covariance matrix of the system it is possible to find a new matrix which has periodicity properties and satisfies a periodic matrix Riceati differential equation; therefore, the time interval of interest, on which the Riceati equation must be solved, will collapse into one period.
Abstract: The main concern of this paper is to determine the state-space representation of a class of linear time-variable, periodic system, such that when excited by stationary white noise it results in a random process with prescribed covariance function. It is shown that by using a proper transformation on the state covariance matrix of the system it is possible to find a new matrix which has periodicity properties and satisfies a periodic matrix Riceati differential equation; therefore, the time interval of interest, on which the matrix Riceati equation must be solved using previous approaches, will collapse into one period.