on the diffusion in a lattice gas model group theoretic approach motivated by some recent results concerning the model of a noninteracting one dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation closed form analytic solutions are found

on the convergence of the generalized aor method abstract we consider the generalized aor method presented by k r james we give some convergence theorems for various kinds of matrices namely when the coefficient matrix of the linear system is positive definite an h l or m matrix or strictly or irreducibly diagonally dominant

advection diffusion past a strip i normal incidence the concentration p x y of particles moving by diffusion and advection or drift is analyzed the motion is impeded by an impenetrable strip that is parallel to the z axis it is assumed that p satisfies the linear advection diffusion equation with a boundary condition on the strip it is also assumed that p 1 at infinity this problem is solved asymptotically for vl d 1 where v is the drift velocity d is the diffusion coefficient and 2l is the strip width it is found that p is large on the side of the strip facing the incident flow that p is small in the shadow behind the strip and that p is nearly constant elsewhere the case of a strip normal to the incident flow is rather different from that of a strip oblique to the flow methods of asymptotic analysis are used

convergence for a general form of the gaor method and its application to the msor method abstract two types of gaor iterative methods were respectively given by a hadjidimos and hu jia gan to solve the linear system ax b where a d e f with d to be nonsingular and diagonal in the former method the parameters involved are two numbers and and in the latter method two diagonal matrices r and the msor iterative method given by d m young is a special case of the latter gaor method for uniformity of the results the paper considers the convergence for a general form of the aor type iteration matrix l r i rl 1 i r l u where l d 1e and u d 1f and gives some important results for the convergence domain of lr when a d e f is an h matrix applying the results to the gaor aor gsor and msor methods we recover certain recent main results and greatly extend certain other previous results

preconditioned accelerated generalized successive overrelaxation method for solving complex symmetric linear systems abstract in this paper by adopting the preconditioned technique for the accelerated generalized successive overrelaxation method agsor proposed by edalatpour et al 2015 we establish the preconditioned agsor pagsor iteration method for solving a class of complex symmetric linear systems the convergence conditions optimal iteration parameters and corresponding optimal convergence factor of the pagsor iteration method are determined besides we prove that the spectral radius of the pagsor iteration method is smaller than that of the agsor one under proper restrictions and its optimal convergence factor is smaller than that of the preconditioned symmetric block triangular splitting psbts one put forward by zhang et al 2018 recently the spectral properties of the preconditioned pagsor matrix are also proposed numerical experiments illustrate the correctness of the theories and the effectiveness of the proposed iteration method and the preconditioner for the generalized minimal residual gmres method

eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems in this paper an indefinite block triangular preconditioner for symmetric saddle point problems is discussed the bounds for all the real eigenvalues of the preconditioned matrix are provided and the bounds for the real and imaginary parts of all the complex eigenvalues of the preconditioned matrix are also provided the corresponding theoretical results of paper by bergamaschi 2012 are improved numerical experiments are reported to confirm our theoretical results

on convergence and semi convergence of ssor like methods for augmented linear systems abstract in this paper we analyze the convergence and semi convergence of a class of ssor like methods with four real functions for augmented systems the class takes most existed ssor like methods as its special cases for nonsingular systems we obtain the minimum of convergence factors of all the ssor like methods in the class and study when it can be reached by the convergence factors of methods in the class by considering the equivalence of methods we show that most of the existed ssor like methods have the same minimum of convergence factors

on parameterized inexact uzawa methods for generalized saddle point problems abstract for the large sparse saddle point problems bai et al recently studied a class of parameterized inexact uzawa piu methods z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 for a special case that the 1 1 block is solved exactly they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method in this paper we develop these methods to the large sparse generalized saddle point problems for the obtained parameterized inexact uzawa method we prove its convergence under suitable restrictions on the iteration parameters in particular we determine its quasi optimal iteration parameters and the corresponding quasi optimal convergence factor for the saddle point problems furthermore this piu method is generalized to obtain a framework of accelerated variants of the parameterized inexact uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation matrix relaxation and inexact iteration

on generalized successive overrelaxation methods for augmented linear systems for the augmented system of linear equations golub wu and yuan recently studied an sor like method bit 41 2001 71 85 by further accelerating it with another parameter in this paper we present a generalized sor gsor method for the augmented linear system we prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor theoretical analyses show that the gsor method has faster asymptotic convergence rate than the sor like method also numerical results show that the gsor method is more effective than the sor like method when they are applied to solve the augmented linear system this gsor method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration besides we also demonstrate a complete version about the convergence theory of the sor like method

on semi convergence of a class of uzawa methods for singular saddle point problems in this paper a class of uzawa methods are presented for singular saddle point problems these methods contain the recently proposed uzawa aor and uzawa saor methods as special cases the 1 1 block of the corresponding uzawa preconditioner is positive definite both nonsingular and singular preconditioning matrices are considered the semi convergence of these methods is analyzed by using the techniques of singular value decomposition and moore penrose inverse numerical results show that they need less workload per iteration step comparing with the gsor and piu methods in some situations so they are feasible and effective for singular saddle point problems in some situations

communication over finite field matrix channels this paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion rather than chosen by an adversary an additive multiplicative matrix channel is considered as a model for random network coding the model assumes that n packets of length m are transmitted over the network and up to t erroneous packets are randomly chosen and injected into the network upper and lower bounds on capacity are obtained for any channel parameters and asymptotic expressions are provided in the limit of large field or matrix size a simple coding scheme is presented that achieves capacity in both limiting cases the scheme has decoding complexity o n 2 m and a probability of error that decreases exponentially both in the packet length and in the field size in bits extensions of these results for coherent network coding are also presented

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

on the brazil nuts problem is it of relevance to hydrodynamics a recent advance in understanding the brazil nuts phenomenon together with insight into the relative motion of different size particles in a lattice fluid makes this phenomenon amenable to an approach based on hydrodynamic concept here we use this conjecture as a stimulus for solving the equation describing asymmetric transport of particles in a medium moving with constant velocity we also consider a method for constructing invariant solutions which enables us to study the dependence of the probability density function on the parameters controlling the asymmetry of the flow physical realizations of the invariant solutions are in agreement with recent computer simulations by alexander and lebowitz

structured preconditioners for nonsingular matrices of block two by two structures for the large sparse block two by two real nonsingular matrices we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations for the specific versions such as modified block jacobi type modified block gauss seidel type and modified block unsymmetric symmetric gauss seidel type preconditioners we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices also we show that when these structured preconditioners are employed to precondition the krylov subspace methods such as gmres and restarted gmres fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two by two coefficient matrices in particular these structured preconditioners can lead to efficient and high quality preconditioning matrices for some typical matrices from the real world applications

semi convergence analysis of uzawa methods for singular saddle point problems recently zheng bai and yang studied the parameterized uzawa method for solving singular saddle point problems b zheng z z bai x yang on semi convergence of parameterized uzawa methods for singular saddle point problems linear algebra appl 431 2009 808 817 in this paper we discuss the inexact uzawa method which covers the uzawa method the preconditioned uzawa method and the parameterized uzawa method to solve the singular saddle point problems we prove the semi convergence result under restrictions by verifying two necessary and sufficient conditions that is all elementary divisors associated with the eigenvalue 1 of its iterative matrix are linear and the pseudo spectral radius of the iterative matrix is less than 1 sufficient conditions for the semi convergence of several uzawa type methods are also provided in addition numerical examples are given to demonstrate the semi convergence of uzawa type methods

a generalization of parameterized inexact uzawa method for singular saddle point problems in this paper we further study the generalized parameterized inexact uzawa method for solving singular saddle point problems obtaining the generalized parameterized inexact uzawa gpiu method theoretical analysis shows that the semi convergence of this new method can be guaranteed by suitable choices of the iteration parameters numerical experiments are used to demonstrate the feasibility and effectiveness of the generalized parameterized inexact uzawa method for solving singular saddle point problems

on the convergence of the maor method abstract in order to solve a linear system ax b hadjidimos et al 1992 defined a class of modified aor maor method whose special case implies the msor method in this paper some sufficient and or necessary conditions for convergence of the maor and msor methods will be achieved when a is a two cyclic matrix and when a is a hermitian positive definite matrix an h l or m matrix and a strictly or irreducibly diagonally dominant matrix the convergence results on the msor method are better than some known theorems the optimum parameters and the optimum spectral radii of the maor and msor methods are obtained which also answers the open problem given by hadjidimos et al

generalized extrapolation principle and convergence of some generalized iterative methods abstract to solve the linear system ax b this paper presents a generalized extrapolated method by replacing the extrapolation parameter with the diagonal matrix and systematically gives the basic results for its convergence based upon these results the paper considers the convergence of the gj and gaor iterative methods and using the set of the equimodularized diagonally similar matrices defined here gives some new further convergence results for h matrices and their subclasses strictly or irreducibly diagonally dominant matrices which unify improve and extend previously given various results finally conditions equivalent to the statement that a is a nonsingular h matrix or a strictly or an irreducibly diagonally dominant matrix are given in connection with the gj and gaor methods

on preconditioned and relaxed avmm methods for quadratic programming problems with equality constraints abstract to iteratively compute a solution of the equality constraint quadratic programming problem by successively introducing relaxation parameters and skillfully adopting a preconditioning matrix we establish a preconditioned and relaxed alternating variable minimization with multiplier pravmm method which is a further generalization of the preconditioned alternating variable minimization with multiplier pavmm method proposed by bai and tao 2016 bit numer math 56 2016 399 422 based on rigorous matrix analysis we demonstrate the asymptotic convergence property of the pravmm method numerical results show that the pravmm method is feasible and effective for solving the equality constraint quadratic programming problems

modified unsymmetric sor method for saddle point problems in this paper we propose a modified unsymmetric sor musor method for solving singular or nonsingular saddle point problem which is an extension of the ssor iteration method for the musor method we prove its convergence for solving nonsingular saddle point problem and semi convergence for solving singular saddle point problem under suitable conditions moreover we study the choices of the optimal parameters numerical experiments are presented which support our theoretical results and reveal that the new method is effective and feasible for solving both singular and nonsingular saddle point problems