In previous studies, the concept of quarter-sweep iteration has been pointed out to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations. Based on the same concept, the essential aim of this paper is to investigate the effectiveness of the Quarter-Sweep Arithmetic Mean (QSAM) method by using the quarter-sweep approximation equation...

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the ...

The integral equation method is widely used for solving many problems in mathematical physics and engineering. This article proposes a computational method for solving nonlinear Fredholm-Volterra integral equations. Several numerical methods for approximating the solution of linear and nonlinear integral equations and specially FredholmVolterra integral equations are known [1-10]. Also, BlockPu...

In an earlier paper (Adv. Appl. Math. 29 (2002), 137–151) on the determinants of certain period matrices, we formulated a conjecture about the determinant of a certain hypergeometric matrix. In this article, we establish this conjecture by constructing a system of linear equations in which that determinant is one of the variables. As a consequence, we obtain the value of an integral which gener...

|This paper discusses eecient solution of dense systems of linear equations arising from integral equation formulations. Several preconditioners in connection with Krylov iterative solvers are examined and compared with LU factorization. Results are shown demonstrating practical aspects and issues we have encountered in implementing iterative solvers on both parallel and sequential computers.

the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

What Is Spectral Theory? By spectral theory we mean the theory of structure of certain bounded linear operators on a Hilbert space. In a broader sense, the history of spectral theory goes way back to the nineteenth century, when the objects of study used to be infinite systems of linear equations and integral equations. The subject was revolutionized in the late 1920s by von Neumann, when he de...

this paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp m-matrix. thefuzzy linear system (fls) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. however, solving this crisp system isdifficult for large n because of dimensionality problems . it is shown that thisdifficulty may be avoide...

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.