Computing generalized inverses using LU factorization of matrix product

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse

MULTIPLE USE OF BACKTRACKING LINE SEARCH IN UNCONSTRAINED OPTIMIZATION

The gradient method is a very efficient iterative technique for solving unconstrained optimization problems. Motivated by recent modifications of some variants of the SM method, this study proposed two methods that are globally convergent as well as computationally efficient. Each of the methods is globally convergent under the influence of a backtracking line search. Results obtained from the numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods

MATLAB SIMULATION OF THE HYBRID OF RECURSIVE NEURAL DYNAMICS FOR ONLINE MATRIX INVERSION

A novel kind of a hybrid recursive neural implicit dynamics for real-time matrix inversion has been recently proposed and investigated. Our goal is to compare the hybrid recursive neural implicit dynamics on the one hand, and conventional explicit neural dynamics on the other hand. Simulation results show that the hybrid model can coincide better with systems in practice and has higher abilities in representing dynamic systems. More importantly, hybrid model can achieve superior convergence performance in comparison with the existing dynamic systems, specifically recently-proposed Zhang dynamics. This paper presents the Simulink model of a hybrid recursive neural implicit dynamics and gives a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model

Application of block Cayley-Hamilton theorem to generalized inversion

In this paper we propose two algorithms for computation of the outer inverse with prescribed range and null space and the Drazin inverse of block matrix. The proposed algorithms are based on the extension of the Leverrier-Faddeev algorithm and the block Cayley-Hamilton theorem. These algorithms are implemented using symbolic and functional possibilities of the packages {\it Mathematica} and using numerical possibilities of {\it Matlab}

A Higher Order Iterative Method for Computing the Drazin Inverse

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper

Application of the Least Squares Solutions in Image Deblurring

A new method for the reconstruction of blurred digital images damaged by separable motion blur is established. The main attribute of the method is based on multiple applications of the least squares solutions of certain matrix equations which define the separable motion blur in conjunction with known image deconvolution techniques. The key feature of the proposed algorithms is reflected in the fact that they can be used only in symbiosis with other image restoration algorithms

COMPUTING TRIANGULATIONS OF THE CONVEX POLYGON IN PHP/MYSQL ENVIRONMENT

In this paper we implement Block method for convex polygon triangulation in web environment (PHP/MySQL). Our main aim is to show the advantages of usage of web technologies in performing complex algorithm from computer graphics. The basic assumption is that one obtained results we store in database and use it for other calculation. Databases are convenient and structured methods of sharing and retrieving data. We have performed a comparative analysis of developed program with respect to two criteria: CPU time in generating triangulation and CPU time in reading results from database

A MODELING FRAMEWORK ON DISTANCE PREDICTING FUNCTIONS FOR LOCATION MODELS IN CONTINUOUS SPACE

Continuous location models are the oldest models in locations analysis dealing with the geometrical representations of reality, and they are based on the continuity of location area. The classical model in this area is the Weber problem. Distances in the Weber problem are often taken to be Euclidean distances, but almost all kinds of the distance functions can be employed. In this survey, we examine an important class of distance predicting functions (DPFs) in location problems all of practical relevance. This paper provides a review on recent efforts and development in modeling travel distances based on the coordinates they use and their applicability in certain practical settings. Very little has been done to include special cases of the class of metrics and its classification in location models and such merit further attention. The new metrics are discussed in the well-known Weber problem, its multi-facility case and distance approximation problems. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions. Research issues which we believe to be worthwhile exploring in the future are also highlighted

A Transformation of Accelerated Double Step Size Method for Unconstrained Optimization

A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition that relates two step lengths in the accelerated double step size gradient descent scheme. The proposed transformation is numerically tested. Obtained results confirm the substantial progress in comparison with the single step size accelerated gradient descent method defined in a classical way regarding all analyzed characteristics: number of iterations, CPU time, and number of function evaluations. Linear convergence of derived method has been proved