A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (...

This paper considers the problem of solving parameter-dependent Riccati equations. In this paper, a tractable iterative scheme involving mainly additions and multiplications is developed for finding solutions to arbitrary accuracy. It is first presented in the parameter-independent case and then extended to the parametric case. It hinges upon two results: (i) a palindromic quadratic polynomial ...

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is basically built on transforming the eq...

The response matrix, consisting of the closed orbit change at each beam position monitor (BPM) due to corrector magnet excitations, was measured and analyzed in order to calibrate a linear optics model of SPEAR. The model calibration was accomplished by varying model parameters to minimize the chi-square difference between the measured and the model response matrices. The singular value decompo...

In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...

A scaling of a nonnegative matrix A is a matrix XA Y -I. where X and Yare nonsingular. nonnegative diagonal matrices. Some condition may be imposed on the scaling, for exa'mple. when A is square, X = Y or det X = det Y. We characterize matrices for ' which there exists a scaling that satisfies predetermined upper and lower bound. Our principal tools are a piecewise linear theorem of the alterna...

Flexible GMRES, introduced by Saad, is a generalization of the standard GMRES method for the solution of large linear systems of equations. It is based on the flexible Arnoldi process for reducing a large square matrix to a small matrix. We describe how the flexible Arnoldi process can be applied to implement one-parameter and multi-parameter Tikhonov regularization of linear discrete ill-posed...

The problem of delay-range-dependent exponential synchronization is investigated for Lur’e master-slave systems with delay feedback control and Markovian switching. Using LyapunovKrasovskii functional and nonsingular M-matrix method, novel delayrange-dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes...

Let e and Σ be respectively the vector of shocks and its variance covariance matrix in a linear system of equations in reduced form. This article shows that a unique orthogonal variance decomposition can be obtained if we impose a restriction that maximizes the trace of A, a positive definite matrix such that e Az = where z is vector of uncorrelated shocks with unit variance. Such a restriction...

In this study, nonlinear vibration of a composite cable is investigated by considering nonlinear stress-strain relations. The composite cable is composed of an aluminum wire as reinforcement and a rubber coating as matrix. The nonlinear governing equations of motion are derived about to an initial curve and based on the fundamentals of continuum mechanics and the nonlinear Green-Lagrangian stra...