this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...

in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...

GMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram–Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating ...

1 CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France ([email protected]). 2 The University of Tennessee, Department of Computer Science, 1122 Volunteer Blvd., Knoxville, TN 37996-3450, USA ([email protected]). 3 Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věž́ı 2, CZ-182 07 Prague 8, Czech Republic ([email protected]). 4 Heinrich-Heine-...

(3) In addition to solutions for | k | ^ 9999, we have solutions, for y ^ 104 and | k | g 99999; there are 1221 for positive k and 799 for negative k. The vast majority of solutions are with y < 100 and Table 2 gives the number of solutions for various ranges of y. The fact that the number of solutions is a rapidly decreasing function of y suggests that for at least some k the solution set may ...

We study decompositions of functions in the Hardy spaces into linear combinations of the basic functions in the orthogonal rational systems {Bn(x)} which can be obtained in the respective contexts through Gram-Schmidt orthogonalization process on shifted Cauchy kernels. Those lead to adaptive decompositions of quaternionic-valued signals of finite energy. This study is a generalization of the m...