We compute the inverse of a speciic innnite r-dimensional matrix, extending a matrix inverse of Krattenthaler. Our inversion is diierent from the r-dimensional matrix inversion recently found by Schlosser but generalizes a multidimensional matrix inversion previously found by Chu. As applications of our matrix inversion we derive some multidimensional q-series identities. Among these are q-anal...

A Generalized Predictive Controller (GPC) for ship track keeping is introduced in this paper. A predictive model for desired heading angles is deduced, the controller is designed based not only on the prediction of the outputs (heading angles), but also on the prediction of the desired heading angles. A recursive algorithm for matrix inversion in the controller is also presented. Applied to car...

The ability to invert large matrices quickly and accurately determines the effectiveness of a computational tool. Current literature suggests that time complexity of matrix inversion is 2 or higher. This paper redesigns the Gauss Jordan algorithm for matrix inversion on a CUDA platform to exploit the large scale parallelization feature of a massively multithreaded GPU. The algorithm is tested f...

Introduction. For a real m×n matrix A, the Moore–Penrose inverse A+ is the unique n×m matrix that satisfies the following four properties: AAA = A , AAA = A , (A+A)T = AA , (AA+)T = AA (see [1], for example). If A is a square nonsingular matrix, then A+ = A−1. Thus, the Moore–Penrose inversion generalizes ordinary matrix inversion. The idea of matrix generalized inverse was first introduced in ...

Langrangian Support Vector Machine (LSVM) and Least Squares Support Vector Machine (LSSVM) are two quick and effective classification methods. In this paper, we first introduce the mathematical models for LSVM and LSSVM and analyze their properties. In the nonlinear case, Sherman-Morrison-Woodbury identity is not used to compute the inversion of a matrix. According to block computation of a mat...

In the presence of spin-orbit coupling and inversion symmetry of the lateral confinement potential a single electron does not exhibit matrix Berry phases in quasi-two-dimensional semiconductor quantum dots. In such a system we investigate whether many-body correlation effects can lead to finite matrix Berry phases. We find that the transformation properties of many-electron wavefunctions under ...

Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...

Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...

In this paper, modified solutions were compared through utilizing three different approximate methods for bar structures. The modifications considered various changes in the initial design. To authors' best of knowledge, the studies have carried out on this matter so far are not broad enough and have considerred the simeltaneous variations of size, geometry and topology on the bar structures. I...

In this paper, a new complex-valued recurrent neural network (CVRNN) called complexvalued Zhang neural network (CVZNN) is proposed and simulated to solve the complexvalued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valu...