Results 331 to 340 of about 649,170 (367)

Approximation schemes for functions of positive-definite matrix values

, 2013
In recent years, there has been an enormous interest in developing methods for the approximation of manifold-valued functions. In this paper, we focus on the manifold of symmetric positive-definite (SPD) matrices.
N. Sharon, Uri Itai
semanticscholar   +1 more source

Enclosing the square root of a positive definite symmetric matrix

International Journal of Computer Mathematics, 1999
The positive definite symmetric square matrices have unique square roots. This paper describes two iterative methods using the concepts of interval analysis for enclosing the square root S of a positive definite symmetric square matrix A. By this, we mean A = S 2. The second method is tested on a numerical example and its results are given. Convergence
Dharmendra Kumar Gupta, C. N. Kaul
openaire   +2 more sources

Positive definite solution of a nonlinear matrix equation

Journal of Fixed Point Theory and Applications, 2016
Using fixed point theory, we present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation \({X = Q \pm \sum^{m}_{i=1}{A_{i}}^*F(X)A_{i}}\), where Q is a positive definite matrix, Ai’s are arbitrary n × n matrices and F is a monotone map from the set of positive definite matrices to itself.
Snehasish Bose, Kallol Paul, Sk. Monowar Hossein   +2 more
openaire   +2 more sources

Multisplitting preconditioners for a symmetric positive definite matrix

Journal of Applied Mathematics and Computing, 2006
We study convergence of multisplitting method associated with a block diagonal conformable multisplitting for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix. Next, we study the validity ofm-step multisplitting polynomial preconditioners which will be used in the preconditioned conjugate
Seyoung Oh, Jae Heon Yun, Eun Heui Kim
openaire   +2 more sources

On positive definite solution of a nonlinear matrix equation

Numerical Linear Algebra with Applications, 2006
AbstractIn this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equationX+A*X−αA=Qwith α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley &
Zhen-yun Peng, Salah M. El-Sayed
openaire   +2 more sources

On positive definite solution of nonlinear matrix equations

Linear and Multilinear Algebra, 2017
AbstractIn this article, we present a sufficient condition for the existence of a unique positive definite solution of the non-linear matrix equation , where , (the set of all Hermitian positive definite matrices), are non-singular matrices and are order-preserving mappings. We give an example of a non-linear matrix equation of the above form (, A is a
Sk. Monowar Hossein, Snehasish Bose, Kallol Paul   +2 more
openaire   +2 more sources

On lower bounds for the smallest eigenvalue of a Hermitian positive-definite matrix

IEEE Transactions on Information Theory, 1995
Presents an improvement to Demho's (1988) lower bound on the smallest eigenvalue of a Hermitian positive-definite matrix. Unlike Dembo's bound the improved bound is always positive. >
E. Ma, C. Zarowski
semanticscholar   +1 more source

Triangular Decomposition of a Positive Definite Matrix Plus a Symmetric Dyad with Applications to Kalman Filtering

, 1972
: An algorithm for the triangular decomposition of the sum of a positive definite matrix and a symmetric dyad is described. Several applications of the algorithm to the implementation of a square root Kalman filter are given.
W. Agee, R. Turner
semanticscholar   +1 more source

High quality preconditioning of a general symmetric positive definite matrix based on its UTU + UTR + RTU-decomposition

Numerical Linear Algebra with Applications, 1998
A new matrix decomposition of the formA = UTU + UTR + RTU is proposed and investigated, where U is an upper triangular matrix (an approximation to the exact Cholesky factor U0), andR is a strictly upper triangular error matrix (with small elements and ...
I. Kaporin
semanticscholar   +1 more source

Triangularization of a positive definite matrix on a parallel computer

Journal of Parallel and Distributed Computing, 1986
Abstract The problem of computing the triangular factors of a square, real, symmetric, and positive definite matrix by using the facilities of a multiprocessor MIMD-type computer is considered. The parallel algorithms based on Cholesky decomposition and Gaussian elimination are derived and analyzed in terms of their speedup and efficiency, when the ...
Janusz S. Kowalik, Swarn P. Kumar
openaire   +2 more sources