on the convergence of a class of parallel decomposition type relaxation methods a class of parallel decomposition type accelerated overrelaxation methods suitable to the simd systems is established and sufficient and or necessary conditions ensuring its convergence are concluded when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and symmetric positive definite matrices

convergent improvement of ssor multisplitting method for an h matrix recently yun jae heon yun convergence of ssor multisplitting method for an h matrix j comput appl math 217 2008 252 258 studied the convergence of the relaxed multisplitting method associated with ssor multisplitting for solving a linear system whose coefficient matrix is an h matrix in this paper we improve the main results of yun s moreover theoretical analysis and numerical examples clearly show that our new convergent domain is wider

comparison results for parallel multisplitting methods with applications to aor methods abstract in this paper we present some comparison theorems between two general parallel multisplittings these comparison theorems can be applied to many classical splittings such as jacobi gauss seidel and aor splittings some significant improvements and generalizations of the existing comparison results are obtained

generalizations of the nonstationary multisplitting iterative method for symmetric positive definite linear systems in this paper we generalize the nonstationary parallel multisplitting iterative method for solving the symmetric positive definite linear systems with several choices of variable weighting matrices the convergence properties of these generalized methods can be improved finally the numerical comparison of several nonstationary parallel multisplitting methods are shown

minimum linear arrangement of chord graphs the minimum linear arrangement minla is a np hard problem in general but there are some classes of graphs optimally solvable in polynomial time in this paper we solve the minimum linear arrangement problem for a new class of graphs chord graphs in polynomial time also we present a closed formula for the cost of optimal arrangement our motivation to solve the problem for this class of graphs is its application in optimization of peer to peer overlay networks

igaor and multisplitting igaor methods for linear complementarity problems in this paper we propose an interval version of the generalized accelerated overrelaxation methods which we refer to as igaor for solving the linear complementarity problems lcp m q and develop a class of multisplitting igaor methods which can be easily implemented in parallel in addition in regards to the h matrix with positive diagonal elements we prove the convergence of these algorithms and illustrate their efficiency through our numerical results

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

incomplete blockwise factorizations of block h matrices the use of incomplete blockwise factorizations as preconditioners in conjugate gradient like methods has become more and more popular in recent years most of the theory concerning existence and applicability of these factorizations has been limited to m matrices so far here we introduce a more general definition of block h matrices robert 8 and we extend the theory to this class of matrices

max norm estimation for the inverse of block matrices abstract maximum norm bound of the inverse of a given matrix is an important issue in a wide range of applications motivated by this fact we will extend the list of matrix classes for which upper bounds for max norms can be obtained these classes are subclasses of block h matrices and they stand in a general position with corresponding point wise classes efficiency of new results will be illustrated by numerical examples

convergence behaviors of multisplitting methods with k 1 relaxed parameters in this paper two multisplitting methods with k 1 relaxed parameters are established for solving a linear system whose coefficient matrix is a large sparse m matrix or h matrix and the corresponding convergence behaviors are studied then the implementation of these two methods with ilu factorizations as inner splittings is investigated finally some numerical experiments are presented to illustrate the effectiveness of the preconditioners obtained from our methods when combined with bicgstab

edge bipancyclicity of star graphs under edge fault tolerant abstract the star graph s n is one of the most famous interconnection networks it has been shown by li t k li cycle embedding in star graphs with edge faults appl math comput 167 2005 891 900 that s n contains a cycle of length from 6 to n when the number of fault edges in the graph does not exceed n 3 in this paper we improve this result by showing that for any edge subset f of s n with f n 3 every edge of s n f lies on a cycle of every even length from 6 to n provided n 3

convergence improvement of relaxed multisplitting usaor methods for h matrices linear systems in this paper based on local relaxed parallel multisplitting usaor lusaor method presented by zhang et al 2008 and similar ideas used by zhang and li 2014 we further analyze local relaxed parallel multisplitting usaor lusaor method and obtain the better convergence results compared to zhang et al s when the system matrix is an h matrix moreover convergence graph and numerical examples clearly show that our new convergence domain is wider

fault tolerant cycle embedding in alternating group graphs abstract cycle embedding is an important issue in evaluating the efficiency of interconnection networks and is also an extension of the theoretical research on hamiltonicity in this paper we study the fault tolerant hamiltonicity of alternating group graphs which were recently proposed as interconnection topologies for parallel and distributed systems a cycle of length l is said to be an l cycle let f be a set of faulty vertices in an n dimensional alternating group graph ag n and let m be the number of vertices in ag n f a previous result in j m chang j s yang y l wang y cheng panconnectivity fault tolerant hamiltonicity and hamiltonian connectivity in alternating group graphs networks 44 2004 302 310 showed that for n 4 ag n f is hamiltonian i e ag n f possesses a hamiltonian cycle if f n 2 and ag n f is hamiltonian connected i e every two vertices of ag n f are connected by a hamiltonian path if f n 3 in this paper we show the following results i ag n f is pancyclic i e ag n f contains an l cycle for each l with 3 l m if f n 2 ii ag n f is vertex pancyclic i e every vertex of ag n f is contained in an l cycle for each l with 3 l m if f n 3 and iii ag n f is edge 4 pancyclic i e every edge of ag n f is contained in an l cycle for each l with 4 l m if f n 4 the first result is an improvement over the previous one and the last two results are new characterization of fault tolerant pancyclicity on ag n all the results we achieved are the best possible in the sense that the number of faulty vertices cannot be increased

an inexact parallel splitting augmented lagrangian method for large system of linear equations parallel iterative methods are powerful in solving large systems of linear equations les the existing parallel computing research results focus mainly on sparse systems or others with particular structure most are based on parallel implementation of the classical relaxation methods such as gauss seidel sor and aor methods which can be efficiently carried out on multiprocessor system in this paper we propose a novel parallel splitting operator method in which we divide the coefficient matrix into two or three parts then we convert the original problem les into a monotone linear variational inequality problem vi with separable structure finally an inexact parallel splitting augmented lagrangian method is proposed to solve the variational inequality problem vi to avoid dealing with the matrix inverse operator we introduce proper inexact terms in subproblems such that the complexity of each iteration of the proposed method is o n 2 in addition the proposed method does not require any special structure of system of les under consideration convergence of the proposed methods in dealing with two and three separable operators respectively is proved numerical computations are provided to show the applicability and robustness of the proposed methods

asynchronous multisplitting two stage iterations for systems of weakly nonlinear equations for the large sparse systems of weakly nonlinear equations arising in the discretizations of many classical differential and integral equations this paper presents a class of asynchronous parallel multisplitting two stage iteration methods for getting their solutions by the high speed multiprocessor systems under suitable assumptions we study the global convergence properties of these asynchronous multisplitting two stage iteration methods moreover for this class of new methods we establish their local convergence theories and precisely estimate their asymptotic convergence factors under some reasonable assumptions when the involved nonlinear mapping is only assumed to be directionally differentiable numerical computations show that our new methods are feasible and efficient for parallely solving the system of weakly nonlinear equations

cycle embedding of augmented cubes a graph g v e is vertex pancyclic if for every vertex u and any integer l ranging from a positive constant l to v g contains a cycle c of length l such that u is in c in this paper we show that an n dimensional augmented cube where n 2 is vertex pancyclic with l 3

chaotic iterative methods for the linear complementarity problems a class of parallel multisplitting chaotic relaxation methods is established for the large sparse linear complementarity problems and the global and monotone convergence is proved for the h matrix and the l matrix classes respectively moreover comparison theorem is given which describes the influences of the parameters and the multiple splittings upon the monotone convergence rates of the new methods

comparison between the variational and implicit differentiation approaches to shape design sensitivities the most commonly used approach to the shape design sensitivity problem results from the implicit differentiation of the discretized equilibrium equations the most general implementation of this technique requires that finite differences be used to differentiate the element stiffness matrices proper choice of the step size is necessary to obtain high levels of accuracy and to avoid round off errors furthermore since it is necessary to operate on the element matrices this method is difficult to implement into a general purpose finite element program a more recent shape design sensitivity formulation based upon variational calculus avoids having to differentiate the discretized equations and results in an analytical expression for the derivative the approach is based upon the total derivative of the variational state equation and uses an adjoint variable technique for design sensitivity analysis only structural response data on the boundary of the structure is necessary thereby making implementation into a general purpose program less difficult this paper attempts to compare the two different techniques and point out the similarities two test problems are shown to demonstrate the accuracy of the variational approach

on structure oriented hybrid two stage iteration methods for the large and sparse blocked system of linear equations in this paper we first present a class of structure oriented hybrid two stage iteration methods for solving the large and sparse blocked system of linear equations as well as the saddle point problem as a special case and the new methods converge to the solution under suitable restrictions for instance when the coefficient matrix is positive stable matrix generally numerical experiments for a model generalized saddle point problem are given and the results show that our new methods are feasible and efficient and converge faster than the classical uzawa method

a class of parallel hybrid two stage iteration methods for block bordered linear systems a class of parallel hybrid two stage iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations and their convergence are proved when the coefficient matrix of this linear system is an m matrix and an h matrix respectively

models of parallel chaotic iteration methods abstract we consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations ax b in the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed in the second model any processor can update the global approximation which resides in the central processor at any time this model is a generalization of a sequential iterative scheme due to ostrowski called the free steering group jacobi iterative scheme and a chaotic relaxation point iterative scheme due to chazan and miranker we show that when a is a monotone matrix and all the splittings are weak regular both models lead to convergent schemes

an optimal time algorithm for minimum linear arrangement of chord graphs a linear arrangement f of an undirected graph g v e with v n nodes is a bijective function f v 0 n 1 the cost function is cost g f email protected u v e f u email protected v and opt g min fcost g f the problem of finding opt g is called minimum linear arrangement minla the minimum linear arrangement is an np hard problem in general but there are some classes of graphs optimally solvable in polynomial time in this paper we show that the label of each node equals to the reverse of binary representation of its id in the optimal arrangement then we design an o n algorithm to solve the minimum linear arrangement problem of chord graphs

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1

convergence theorems for parallel alternating iterative methods the parallel multisplitting nonstationary iterative model a was introduced by bru elsner and neumann linear algebra appl 103 1988 175 192 for solving nonsingular linear system ax b using a weak nonnegative multisplitting of the first type in this paper new results using a weak nonnegative multisplitting of the second type are introduced when a is a monotone matrix and using p regular multisplitting when a is a symmetric positive definite matrix combining model a and alternating iterative methods two new models of parallel multisplitting nonstationary iterations are introduced it is shown that when matrix a is monotone and the multisplittings are weak nonnegative of the first or second type both models lead to convergent schemes when matrix a is symmetric positive definite and the multisplittings are p regular the schemes are also convergent

convergence properties of preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite matrices for the non hermitian and positive semidefinite systems of linear equations we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned hermitian and skew hermitian splitting iteration methods we then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned hermitian and skew hermitian splitting iteration methods

grpm style methods and comparisons of convergent and divergent rates relaxed technique is one of techniques for improving convergence rate of splitting iterative methods based on local relaxed method and system relaxed method of parallel multisplitting frommer and mayer a frommer g mayer convergence of relaxed parallel multisplitting methods linear algebra appl 119 1989 141 152 we give the global relaxed parallel multisplitting grpm method by introducing some relaxed parameters and study the convergence of our methods grpm style when the coefficient matrices are h matrices numerical experiments show that when choosing the approximately optimal relaxed parameters our methods have faster convergent rate than the methods in chang d w chang convergence analysis of the parallel multisplitting tor methods j comput appl math 72 1996 169 177 frommer and mayer a frommer g mayer convergence of relaxed parallel multisplitting methods linear algebra appl 119 1989 141 152 furthermore the convergent and divergent rates of local relaxed parallel multisplitting lrpm style methods about multislitting tor aor sor g s extraolated jacobi methods as well as jacobi iterative method are compared in detail

variational principle for shape design sensitivity analysis in this paper the adjoint method of design sensitivity analysis is stated as a general variational principle that is applicable to a wide range of problems the principle gives a very simple and straightforward method of obtaining the design sensitivity expression for a functional dependent on the state fields the sensitivity expression involves certain adjoint fields and explicit design variations of the functional and the governing equations for the primary state fields the principle is stated in terms of an augmented functional that is defined by adding to the response functional whose sensitivity is desired the equilibrium equation of the primary problem then explicit design variation of the augmented functional gives the total design variation of the response functional stationarity of the augmented functional with respect to the state fields defines the adjoint problem for the response functional the principle is proved and applied to several classes of linear and nonlinear problems such as field problems structural problems and dynamic response problems it is shown that the design sensitivity expressions derived in the literature using long procedures are obtained quite routinely by use of the principle

a sensitivity interpretation of adjoint variables in optimal design abstract the adjoint method of computing derivatives of cost and constraint functions with respect to design variables requires the calculation of certain adjoint variables until now the adjoint variables have been looked upon only as some intermediate vectors needed to calculate design derivatives in this paper they are shown to have an important significance they represent the sensitivity of the cost and constraint functions with respect to the loading or forcing function in the design problem a sensitivity theorem for the adjoint variables is presented for structural mechanical dynamic and distributed parameter systems these results offer some immediate practical advantages such as a method for computing influence coefficients for structural systems and a method for verifying debugging the analytical calculation of adjoint variables in development of a computer code

layout of random circulant graphs abstract a circulant graph g is a graph on n vertices that can be numbered from 0 to n 1 in such a way that if two vertices x and x d mod n are adjacent then every two vertices z and z d mod n are adjacent we call layout of the circulant graph any numbering that witness this definition a random circulant graph results from deleting each edge of g uniformly with probability 1 p we address the problem of finding the layout of a random circulant graph we provide a polynomial time algorithm that approximates the solution and we bound the error of the approximation with high probability

the block preconditioned lsqr and gl lsqr algorithms for the block partitioned matrices in this paper a new block preconditioner is proposed for the block partitioned matrices this preconditioner is based on the block c orthogonalization where c is a symmetric positive definite matrix the block preconditioned least squares bpls and block preconditioned global least squares bpgls algorithms are presented to solve the linear system of equations with block partioned coefficient matrix and multiple linear system of equations respectively the bpls algorithm is applied to solve the complex linear system of equations and also bpls and classical preconditioned least squares pls algorithms are compared finally some numerical experiments are given to show the efficiency of the new block preconditioner

on the convergence of some generalized iterative methods abstract this paper is concerned with the generalized accelerated overrelaxation gaor method which constitutes a generalization of the basic iterative methods for the solution of linear systems a number of new theoretical results are presented concerning the convergence theory of the gaor method and special cases of it much attention is given to linear systems with positive definite coefficient matrices although the problem of determining the various optimum parameters of the gaor method in the general case is very difficult to solve theoretically and is still an open one the numerical examples which are presented in this paper show that a suitable exploitation of it may give much better results than the other basic iterative methods

parallel multisplitting explicit aor methods for numerical solutions of semilinear elliptic boundary value problems abstract a class of parallel multisplitting explicit aor methods for a large scale system of nonlinear algebraic equations which is a finite difference approximation of a semilinear elliptic boundary value problem are presented this class of methods avoid the inner iteration and are shown to converge monotonically either from above or from below to a solution of the system without the monotonicity property of nonlinearity moreover this class of methods are applicable to the pure neumann boundary value problems a sufficient condition for the uniqueness of the solutions is provided the global convergence of the methods and the influence of the acceleration factor on the convergence rate are considered the applications and numerical results are given

variational method for design sensitivity analysis in nonlinear structural mechanics this paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape nonshape and material selection problems the concepts of reference volume and adjoint structure are used to develop the unified viewpoint a general formula for design sensitivity analysis is derived several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure

a class of parallel decomposition type relaxation methods for large sparse systems of linear equations abstract a class of parallel decomposition type accelerated over relaxation methods including four arbitrary parameters and suitable to the simd systems is established for solving the large sparse systems of linear equations in this paper and sufficient conditions ensuring its convergence are deduced when the coefficient matrices of the linear systems of equations are respectively l matrices h matrices and positive definite matrices in particular we investigate in detail the symmetric versions of these new methods and deduce a series of conveniently applicable conditions for determining the convergence of hese versions when the coefficient matrices of the linear systems of equations are symmetric positive definite matrices

a class of asynchronous parallel iterations for the systems of nonlinear algebraic equations abstract asynchronous parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations a x t x b with a t l r n being matrices having particular properties r n r n being diagonal and continuous mappings and b r n a known vector and their global convergence and asymptotic convergence rates are investigated in detail under some reasonable conditions

on the parallel gsaor method for block diagonally dominant matrices in this paper we consider the parallel generalized saor iterative method based on the generalized aor iterative method presented by james for solving large nonsingular system we obtain some convergence theorems for the case when coefficient matrix is a block diagonally dominant matrix or a generalized block diagonal dominant matrix a numerical example is given to illustrate to our results

on the convergence of the parallel multisplitting aor algorithm abstract we present a class of relaxed parallel multisplitting algorithms called the parallel multisplitting aor algorithm for solving large nonsingular systems of equations ax b this new algorithm is a generalization and improvement of the relaxed parallel multisplitting method linear algebra appl 119 141 152 1989 based on the new algorithm model we establish another algorithm called the relaxed parallel multisplitting aor algorithm the convergence of these algorithms is discussed under the condition that a is a monotone matrix we obtain corresponding convergence results these convergence conditions are convenient to verify

parallel nonlinear aor method and its convergence abstract we set up a class of parallel nonlinear aor method in the sense of matrix multi splitting for solving the large scale system of nonlinear equations ax x b with a l rn nonsingular b rn and rn rn being continuously diagonal the global as well as the monotone convergence of this method is proved