group accelerated overrelaxation methods on rotated grid in martins et al m m martins w s yousif d j evans explicit group aor method for solving elliptic partial differential equations neural parallel and science computation 10 4 2002 411 422 a new explicit four point group accelerated overrelaxation group aor iterative method was presented where the computational superiority of this new technique was established when compared with the point aor method developed by evans and martins d j evans m m martins the aor method for ax xb c international journal of computer mathematics 52 1994 75 82 and martins et al m m martins d j evans m e trigo the aor iterative method for new preconditioned linear systems journal of computational and applied mathematics 132 2001 461 466 in this work we formulate an alternative group scheme from the aor family derived from the rotated skewed five point formula g dahlquist a bjorck numerical methods prentice hall englewood cliffs nj 1974 p 320 y saad iterative methods for sparse linear systems second ed pws publishing company boston 2000 p 50 the derivation of this new group scheme is presented and its performance is compared with the existing explicit four point group aor we include the analysis of the convergence results for the new group scheme numerical experiments are also presented to illustrate our results

a class of preconditioners based on the i s α type preconditioning matrices for solving linear systems abstract the purpose of this paper is to present a class of preconditioners based on the i s type preconditioning matrices provided by evans et al d j evans m m martins m e trigo the aor iterative method for new preconditioned linear systems j comput appl math 132 2001 461 466 and zhang et al y zhang t z huang x p liu modified iterative methods for nonnegative matrices and m matrices linear systems comput math appl 50 2005 1587 1602 three mathematical models are presented to seek the optimal parameter for these preconditioners numerical results are presented which show the improvements on the convergence rate of the jacobi type and gauss seidel type preconditioned iterative methods

a variant of the aor method for augmented systems in this paper we present a variant of the accelerated overrelaxation iterative method aor denoted by modified aor like method maor like method for solving the augmented systems i e the aor like method with three real parameters r and for special values of r and we get the msor like method the aor like method and the sor like method an equation relating the involved parameters and the eigenvalues of the iteration matrix of the maor like method is obtained furthermore some convergence conditions for the maor like method are derived this paper generalizes the main results of li li nie and evans 2004 and shao li and li 2007 numerical examples are presented to show that for a suitable choice of the involved parameters the maor like method is superior when compared to the above iterative methods and to the ssor like method presented by zheng wang and wu 2009

improving jacobi and gauss seidel iterations abstract when convergent jacobi or gauss seidel iterations can be applied to solve systems of linear equations a natural question is how convergence rates are affected if the original system is modified by performing some gaussian elimination we prove that if the initial iteration matrix is nonnegative then such elimination improves convergence our results extend those contained in 4

comparison theorems of preconditioned gauss seidel methods for m matrices in this paper a new preconditioner for the gauss seidel method is proposed for solving linear systems whose coefficient matrix is an m matrix several comparison theorems are shown for the proposed method with several preconditioners it follows from the comparison results that our preconditioner is one of the best preconditioners in the sense of convergence rate finally numerical examples are given to illustrate our theoretical results two conjectures are proposed as well based on our numerical tests

losses in the pemc boundary perfect electromagnetic conductor pemc was recently introduced to generalize both the perfect electric conductor pec and the perfect magnetic conductor pmc which are used as boundary material in this paper an extension of pemc boundary conditions is made to a more realistic model with small losses good electromagnetic conductor it is shown that the antisymmetric boundary impedance dyadic defining the ideal pemc boundary cannot alone carry any losses and a symmetric component must be added that actually dominates the lossy behavior of the boundary as an example a slab of low loss gyrotropic wave guiding material is studied and shown to represent the lossy counterpart of the pemc boundary the effect of losses is demonstrated by considering plane wave reflection from an imperfect pemc plane

the aor iterative method for new preconditioned linear systems 461 abstract in this paper we apply the aor method to preconditioned linear systems different from those considered in evans and martins internat j comput math 5 1995 69 76 gunawardena et al linear algebra appl 154 156 1991 123 143 and li and evans technical report no 901 department of computer studies university of loughborough 1994 our results show that some improvements in the convergence rate of this iterative method can be obtained

green s function extraction for interfaces with impedance boundary conditions theory and experiments to obtain the response between two receivers from cross correlations of wave fields recorded at these receivers are well established the principle relies on mutually spatial and temporal uncorrelated contributions from sources on a boundary enclosing the two receivers which upon cross correlation interfere only constructively for signals traveling between the two receivers it has therefore become generally known as interferometry the theory includes situations with flow mechanical and electromagnetic field fluctuations and their mutual coupling here we present an electromagnetic theory for green s function retrieval from cross correlations that incorporates general bianisotropic media in which interfaces are present where bianisotropic impedance boundary conditions apply the derived green s function representation shows that in lossless media and for interfaces with lossless impedance boundary conditions the green s function between two receivers is obtained by cross correlating the recordings of these receivers from sources on a boundary enclosing them we show numerical examples in 2 d where proper solutions are numerically tractable and practical approximations illustrate that numerically less intensive algorithms lead to acceptable results and accurate extraction of reflections from impedance boundary surfaces because the method is data driven it is suitable for experimental green s function extraction from measured data

improvements of preconditioned aor iterative method for l matrices in this paper we improve the preconditioned aor method of linear systems considered by evans et al the aor iterative method for new preconditioned linear systems comput appl math 132 2001 461 466 in evans paper the coefficient matrix of linear system have to be an l matrix with a i i 1a i 1 i 0 i 1 n 1 and 0

iterative numerical solution of non linear integro differential equations by the tau method abstract in this paper we try to give an iterative application of the operational tau method e l ortiz h samara an operational approach to the tau method for the numerical solution of non linear differential equations computing 27 1981 15 25 for the numerical solution of non linear integro differential nide a simple method convert non linear equations to linear equations then we use the operational tau method for the numerical solution of linearized equation iteratively various numerical examples illustrate the accuracy of the method

an iteration method for solving the linear system ax b abstract in this paper based on a convergence splitting of the matrix a we present an inner outer iteration method for solving the linear system a x b we analyze the overall convergence of this method without any other restriction on its parameters moreover we give the accelerated inner outer iteration method and discuss how to apply the inner outer iterations as a preconditioner for the krylov subspace methods the inner outer iteration method can also be used for the solution of a x b c finally several numerical examples are given to validate the performance of our proposed algorithms

modified iterative methods for consistent linear systems abstract in order to solve a linear system ax b certain elementary row operations are performed on a before applying the gauss seidel or jacobi iterative methods it is shown that when a is a nonsingular m matrix or a singular tridiagonal m matrix the modified method yields considerable improvement in the rate of convergence for the iterative method it is also shown that in some cases this method is superior to certain other modified iterative methods the performance of this modified method on some matrices other than m matrices is also investigated

preconditioned aor iterative methods for m matrices linear systems with m matrices often appear in a wide variety of areas in this paper we give general preconditioners for solving the systems with nonsingular m matrix we show that our preconditioners increase the convergence rate of aor iterative methods numerical results for corresponding preconditioned gmres methods are also given

transformation method for problems involving perfect electromagnetic conductor pemc structures perfect electric conductor pec and perfect magnetic conductor pmc can be generalized to perfect electromagnetic conductor pemc a medium where certain linear combinations of electromagnetic fields are required to vanish in differential form representation the corresponding medium is characterized as the simplest possible medium it is defined through a scalar admittance parameter whose zero and infinite limits yield the pmc and pec media respectively in this paper a duality transformation is found that has the property of transforming pemc to pec and an isotropic medium to itself thus problems involving pemc objects in air can be transformed to problems with pec objects in air which can be solved through traditional techniques and then transformed back several simple examples are treated to demonstrate the principle pemc has the potential of having similar applications as pmc in antenna engineering and finding structures for its realization is a challenge

modified iterative methods for nonnegative matrices and m matrices linear systems the purpose of this paper is to present new preconditioning techniques for solving nonnegative matrices linear system and m matrices linear system ax b based on the i s a type preconditioning matrices provided by hadjidimos et al 1 and evans et al 2 convergence analysis of the proposed methods are given numerical results are presented which show the improvements on the convergence rate of the jacobi type and gauss seidel type preconditioned iterative methods

comparison results of the preconditioned aor methods for l matrices abstract in this paper we first provide comparison results of several types of the preconditioned aor paor methods for solving a linear system whose coefficient matrix is an l matrix satisfying some weaker conditions than those used in the recent literature next we propose an application of paor method to a preconditioner of krylov subspace method lastly numerical results are provided to show that krylov subspace method with the paor preconditioner performs quite well as compared with the ilu 0 preconditioner

the jacobi and gauss seidel type iteration methods for the matrix equation a x b c in this paper the jacobi and gauss seidel type iteration methods are proposed for solving the matrix equation a x b c which are based on the splitting schemes of the matrices a and b the convergence and computational cost of these iteration methods are discussed furthermore we give the preconditioned jacobi and gauss seidel type iteration methods numerical examples are given to demonstrate the efficiency of these methods proposed in this paper

numerical solution of a class of integro differential equations by the tau method with an error estimation the tau method by construction produces approximate polynomial solutions of differential equations the purpose of this paper is to extend the tau method to the integro differential equations an efficient error estimation for the tau method is also introduced details of this method are presented and some numerical results along with estimated errors are given to clarify the method and its error estimator

gauss type preconditioning techniques for linear systems abstract many researchers have considered preconditioners chosen to eliminate the off diagonal elements of the coefficient matrix of a linear system in this work we generalize the left gauss type preconditioners y zhang t z huang x p liu modified iterative methods for nonnegative matrices and m matrices linear systems comput math appl 50 2005 1587 1602 which eliminate the strictly lower triangular elements right gauss type preconditioners that eliminate strictly upper triangular elements are proposed in this paper these gauss type preconditioners are partly derived from the lu factorization method theoretic analysis on spectral radii of the two kinds of gauss type preconditioners is given numerical experiments are used to show the performance of the improved inbuilt left and right gauss type preconditioning algorithms associated with jacobi type and gauss seidel type iterative methods

solving fredholm integro differential equations using reproducing kernel hilbert space method in this study the numerical solution of fredholm integro differential equation is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the initial condition of the problem is satisfied the exact solution ux is represented in the form of series in the space w 2 2 a b in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 2 a b some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear fredholm integro differential equations