Integral equation has been one of the essential tools for various areas of applied mathematics. The aim of this article is to propose a simple, accurate and efficient iterative method for obtaining solutions for Fredh...
详细信息
Integral equation has been one of the essential tools for various areas of applied mathematics. The aim of this article is to propose a simple, accurate and efficient iterative method for obtaining solutions for Fredholm integral equation systems of one dimension of the second kind. The proposed numerical method is based on orthogonal triangular functions. The orthogonal Triangular Functions (TFs) based method is first applied to transform the Fredhoim system of integral equations to four coupled system of matrix algebraic equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of an approximate numerical solution of the unknown solution functions of the integral problems. Some examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other numerical methods and the exact solutions.
An iterativealgorithm is presented for solving the extended Sylvester-conjugate matrix equation. By this iterative method, the solvability of the matrix equation can be determined automatically. When the matrix equat...
详细信息
An iterativealgorithm is presented for solving the extended Sylvester-conjugate matrix equation. By this iterative method, the solvability of the matrix equation can be determined automatically. When the matrix equation is consistent, a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general complex matrix equation. Two numerical examples are given to illustrate the effectiveness of the proposed methods. (C) 2011 Elsevier Ltd. All rights reserved.
An iterativealgorithm is constructed to give a common solution to a group of complex matrix equations. By using the proposed algorithm, the existence of a common solution can be determined automatically. When a commo...
详细信息
An iterativealgorithm is constructed to give a common solution to a group of complex matrix equations. By using the proposed algorithm, the existence of a common solution can be determined automatically. When a common solution exists for this group of matrix equations, it is proven by using a real inner product in complex matrix spaces as a tool that a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general case. A numerical example is given to illustrate the effectiveness of the proposed method. (C) 2011 Elsevier Inc. All rights reserved.
In this note, a technical error is pointed out in the proof of a lemma in the above paper. A correct proof of this lemma is given. In addition, a further result on the algorithm in the above paper is also given. Copyr...
详细信息
In this note, a technical error is pointed out in the proof of a lemma in the above paper. A correct proof of this lemma is given. In addition, a further result on the algorithm in the above paper is also given. Copyright (C) 2009 John Wiley & Sons, Ltd.
暂无评论