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

rank based analysis of the heteroscedastic linear model abstract heteroscedasticity often causes problems in the analysis of linear models frequently for such cases scale is a function of the response here for such models a methodology is presented based on well known rank based procedures the procedure is iterative using the residuals from an initial r estimate of the regression coefficients scale is estimated by inverting a linear rank test for scale this in turn leads to a weighted r estimate of the regression coefficients and then to a final estimate of scale asymptotic linearity results for these estimates are derived from which their asymptotic distribution is obtained the weighted r estimate has the same asymptotic distribution as the optimal known scale r estimate hence it is efficiently robust consistent estimates of the standard errors of the r estimates of scale and the regression coefficients are determined based on these results a complete inference for the regression coefficients and the scale parameter is realized including a

block gauss elimination followed by a classical iterative method for the solution of linear systems in the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the gauss elimination process in the hope that this will increase the rates of convergence of the iterative method this combination of methods has been proven successful especially when the matrix a of the system is an m matrix the purpose of this paper is to extend the idea of one to more gauss elimination steps consider other classes of matrices a e g p cyclic consistently ordered and generalize and improve the asymptotic convergence rates of some of the methods known so far

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

improving jacobi methods for nonnegative h matrices linear systems abstract in this paper we consider a preconditioned iterative method for solving linear system ax b which is a generalization of method proposed by 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 and prove its convergence for the case when a is a nonnegative h matrix numerical examples are also given which show the effectiveness of our method

a five field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity a novel hu washizu type 5 field virtual work principle for nearly inextensible and almost incompressible finite hyperelasticity is developed and implemented the formulation is implemented in an hp adaptive code providing the proper flexible environment for finite elements with variable order and mixed interpolation the novel implementation includes residual based error estimation and mesh adaptivity in the fully constrained limit the formulation provides the constraint manifold setting of hyperelasticity with the simple internal kinematic constraints of inextensibility and incompressibility a study using a semi inverse analytical solution and h refinements and p enrichments corroborates the convergence characteristics of the 5 field implementation a new closed form solution for pure torsion of a circular cylindrical tube with inextensible fibres is derived and used for verification as typical applications are found in e g soft tissue biomechanics passive pressurisation of an ellipsoidal geometry resembling the left ventricle of a rabbit heart is analysed to demonstrate the capability of modelling transversely isotropic materials

some new estimation methods for weighted regression where there are possible outliers the problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model we treat the situation in which the variance is a function of the explanatory variables to estimate robustly the variance in this case it is necessary to guard against the influence of outliers in the design as well as outliers in the response by analogy with the homoscedastic regression case we propose two estimators that do this their performances are evaluated on a number of data sets we had considerable success with estimators that bound the self influence that is the influence an observation has on its own fitted value we conjecture that in other situations e g homoscedastic regression bounding the selfinfluence will lead to estimators with good robustness properties

preconditioned gaor methods for solving weighted linear least squares problems in this paper we present the preconditioned generalized accelerated overrelaxation gaor method for solving linear systems based on a class of weighted linear least square problems two kinds of preconditioning are proposed and each one contains three preconditioners we compare the spectral radii of the iteration matrices of the preconditioned and the original methods the comparison results show that the convergence rate of the preconditioned gaor methods is indeed better than the rate of the original method whenever the original method is convergent finally a numerical example is presented in order to confirm these theoretical results

more on modifications and improvements of classical iterative schemes for m matrices in the last four decades many articles have been devoted to the modifications and improvements of classes of preconditioners for linear systems whose matrix coefficient is an m matrix in order to improve on the convergence rates of the classical iterative schemes jacobi gauss seidel etc the present work is a contribution towards the generalization of the most common preconditioners used so far

letter to the editor comment on a comparison theorem of the sor iterative method in this work we point out that there are incorrect assertions in the article by li ying sun li ying sun a comparison theorem for the sor iterative method j comput appl math 181 2005 336 341 moreover we answer an open problem

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

improving aor method for consistent linear systems abstract milaszewicz j p milaszewicz improving jacobi and gauss seidel iterations linear algebra appl 93 1987 161 170 and gunawardena et al a d gunawardena s k jain l snyder modified iteration methods for consistent linear systems linear algebra appl 154 156 1991 123 143 presented preconditioned methods for linear system in order to improve the convergence rates of jacobi and gauss seidel iterative schemes respectively in this paper we apply aor and sor iterative schemes to the preconditioned linear systems and provide two theorems to improve the convergence rates of these iterative methods meanwhile the methods in this paper can be used to more class of linear systems

convergence of two stage and multisplitting methods using various types of splittings we first study the convergence of both two stage iterative method and multisplitting methods using various types of splittings for solving a linear system whose coefficient matrix is an m matrix or an h matrix we next study a parallel implementation of two stage multisplitting method associated with a special multisplitting and an application of the two stage multisplitting method to parallel preconditioner of krylov subspace methods lastly we provide parallel performance results of both two stage multisplitting method and krylov subspace method with a parallel preconditioner which is derived from two stage multisplitting method on the ibm p690 supercomputer

erratum to a note on the preconditioned gauss seidel method for m matrices j comput appl math 219 1 2008 59 71 in this note some errors in a recent article by niki et al h niki t kohno m morimoto the preconditioned gauss seidel method faster than the sor method j comput appl math 219 2008 59 71 are pointed out and a new proof for the corresponding result is presented

scheduled relaxation jacobi method elliptic partial differential equations epdes appear in a wide variety of areas of mathematics physics and engineering typically epdes must be solved numerically which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution the scheduled relaxation jacobi srj is a promising class of methods atypical for combining simplicity and efficiency that has been recently introduced for solving linear poisson like epdes the srj methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances the efficiency in the reduction of the residual increases with the number of levels employed in the algorithm applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal srj schemes as the mixed non linear algebraic differential system of equations from which they result becomes notably stiff here we present a new methodology for obtaining the parameters of srj schemes that overcomes the limitations of the original algorithm and provide parameters for srj schemes with up to 15 levels and resolutions of up to 215 points per dimension allowing for acceleration factors larger than several hundreds with respect to the jacobi method for typical resolutions and in some high resolution cases close to 1000 most of the success in finding srj optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations furthermore we extend the original algorithm to apply it to certain systems of non linear epdes we compute new optimal parameters of the scheduled relaxation jacobi method the new parameters are calculated for srj schemes with p 6 to p 15 levels we reduce the stiffness in the computation of optimal srj parameters analytically we provide a grid of optimal parameters for different p and numerical resolutions we benchmark srj methods against other algorithms to solve linear systems

the convergence of the modified gauss seidel methods for consistent linear systems in this paper we present a convergence analysis for the modified gauss seidel methods given in gunawardena et al linear algebra appl 154 156 1991 125 and kohno et al linear algebra appl 267 1997 113 for consistent linear systems we prove that the modified gauss seidel method converges for some values of the parameters in the preconditioned matrix

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

letter to the editor a note on the preconditioned gauss seidel gs method for linear systems wen li j comput appl math 182 2005 81 90 asserted that there are some errors in article by hiroshi niki kyouji harada munenori morimoto and michio sakakihara j comput appl math 164 165 2004 587 600 and li presented a new proof for the corresponding results in h niki et al in this paper we point out some errors in li s assertion moreover we show that a new proof presented by li is imperfect

two new modified gauss seidel methods for linear system with m matrices in 2002 h kotakemori et al proposed the modified gauss seidel mgs method for solving the linear system with the preconditioner p i s m a x h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x j comput appl math 145 2002 373 378 since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix the preconditioning effect is not observed on the nth row in the present paper to deal with this drawback we propose two new preconditioners the convergence and comparison theorems of the modified gauss seidel methods with these two preconditioners for solving the linear system are established the convergence rates of the new proposed preconditioned methods are compared in addition numerical experiments are used to show the effectiveness of the new mgs methods

a note on the preconditioner pm i sm kotakemori et al h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x journal of computational and applied mathematics 145 2002 373 378 have reported that the convergence rate of the iterative method with a preconditioner p m i s m was superior to one of the modified gauss seidel method under the condition these authors derived a theorem comparing the gauss seidel method with the proposed method however through application of a counter example wen li wen li a note on the preconditioned gaussseidel gs method for linear systems journal of computational and applied mathematics 182 2005 81 91 pointed out that there exists a special matrix that does not satisfy this comparison theorem in this note we analyze the reason why such a to counter example may be produced and propose a preconditioner to overcome this problem

regression diagnostics for rank based methods abstract residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model in this article we explore the properties of the residuals from a rank based fit of the model we present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank based fit we show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model furthermore our diagnostic techniques inherit the excellent efficiency properties of the rank based fit over a wide class of error distributions including asymmetric distributions we illustrate these techniques with several examples

p fems for hyperelastic anisotropic nearly incompressible materials under finite deformations with applications to arteries simulation the displacement formulation of p fems is extended to nearly incompressible hyper elastic anisotropic materials under finite deformations in a three dimensional setting to demonstrate the efficiency and accuracy of the formulation we derive analytical solutions that serve for the verification of the p fe results the locking free properties at the limit of incompressibility the high convergence rates and the robustness with respect to large aspect ratios of the p fes are demonstrated by numerical experiments and compared in terms of degrees of freedom and cpu times to equivalent classical formulations using h fems p fems are then exploited to investigate artery like structures having complex constitutive models and particularly the influence of slight allowable compressibility of orders of several percents on the stress levels copyright 2011 john wiley sons ltd

comparison results for solving preconditioned linear systems in this paper we present some comparison theorems between two different modified gauss seidel mgs methods the second preconditioning based on the first preconditioning is also discussed in this paper

some new preconditioned generalized aor methods for generalized least squares problems in this paper we present some new preconditioned gaor methods for solving generalized least squares problems and their comparison results comparison results show that the convergence rates of the new preconditioned gaor methods are better than those of the preconditioned gaor methods presented by zhou et al 2009 19 and wang et al 2013 18 whenever these methods are convergent lastly numerical experiments are provided to confirm the theoretical results

an extended gs method for dense linear systems davey and rosindale k davey i rosindale an iterative solution scheme for systems of boundary element equations internat j numer methods engrg 37 1994 1399 1411 derived the gsor method which uses an upper triangular matrix w in order to solve dense linear systems by applying functional analysis the authors presented an expression for the optimum w moreover davey and bounds k davey s bounds a generalized sor method for dense linear systems of boundary element equations siam j comput 19 1998 953 967 also introduced further interesting results in this note we employ a matrix analysis approach to investigate these schemes and derive theorems that compare these schemes with existing preconditioners for dense linear systems we show that the convergence rate of the gauss seidel method with preconditioner p g is superior to that of the gsor method moreover we define some splittings associated with the iterative schemes some numerical examples are reported to confirm the theoretical analysis we show that the egs method with preconditioner p g c o p t produces an extremely small spectral radius in comparison with the other schemes considered

a comparison theorem for the sor iterative method in 1997 kohno et al have reported numerically that the improving modified gauss seidel method which was referred to as the imgs method is superior to the sor iterative method in this paper we prove that the spectral radius of the imgs method is smaller than that of the sor method and gauss seidel method if the relaxation parameter w 0 1 as a result we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods some recent results are improved

a novel computational formulation for nearly incompressible and nearly inextensible finite hyperelasticity abstract a novel approach to computational almost inextensible transversely isotropic and nearly incompressible finite hyperelastic fibre mechanics is introduced it relies on using an equivalent generalised right cauchy green stretch tensor which is volume preserving and simply stretch free in the limit of incompressibility and inextensibility in other words its third and fourth principal invariants become trivial otherwise it represents volume change and fibre stretch with the aid of point wise equivalent auxiliary measures in the continuous case the generalised kinematics implies the usual orthogonal spherical deviatoric decomposition of the stresses the deviatoric stresses are further orthogonally decomposed into axial fibre and ground substance stresses the novel approach implies that the deviatoric ground substance stresses are trivial in the fibre direction as opposed to the current standard formulation the approach is also able to represent exact inextensible fibres which is a problem recently addressed in the literature using an additive volumetric isochoric decoupled strain energy density function relying on volume preserving stretch the formulation is corroborated by a couple of numerical examples using a preliminary finite element setting the basis for the implementation is provided

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

convergence of the preconditioned aor method for irreducible l matrices in this paper we first point out some errors in a recent article by li et al y li c li s wu improving aor method for consistent linear systems appl math comput 186 2007 379 388 and then we provide some correct results for convergence of the preconditioned aor method for irreducible l matrices lastly we provide numerical experiments to illustrate the theoretical results

accelerated iterative method for z matrices it has recently been reported that the convergence of the preconditioned gauss seidel method which uses a matrix of the type i u as a preconditioner is faster than the basic iterative method in this paper we generalize the preconditioner to the type i bu where b is a positive real number after discussing convergence of the method applied to z matrices we propose an algorithm for estimating the optimum b numerical examples are also given which show the effectiveness of our algorithm

study on the preconditioners i sm kotakemori et al 2002 2 have reported that the convergence rate of the iterative method with a preconditioner p m i s m a x was superior to one of the modified gauss seidel methods under a special condition the authors derived a theorem comparing the gauss seidel method to remove the requirement for this condition morimoto et al 2004 4 have proposed the preconditioner p s m i s s m however it is pointed out that there exists a special matrix that does not satisfy this comparison theorem to overcome this problem kohno et al 2009 3 have proposed some preconditioners in this note we present a new preconditioner and from numerical results we show that the convergence rate of the proposed method is better than that of the gauss seidel method with other preconditioners in addition we presented the comparison theorem for the proposed preconditioner we succeeded to overcome two drawbacks mentioned above

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

a comparison theorem for the iterative method with the preconditioner i s max in 1991 gunawardena et al linear algebra appl 154 156 1991 123 have reported the modified gauss seidel method with a preconditioner i s in this article we propose to use a preconditioner i smax instead of i s here smax is constructed by only the largest element at each row of the upper triangular part of a by using the lemma established neumann and plemmons linear algebra appl 88 89 1987 559 we get the comparison theorem for the proposed method simple numerical examples are also given

improving the modified gauss seidel method for z matrices abstract in 1991 a d gunawardena et al reported that the convergence rate of the gauss seidel method with a preconditioning matrix i s is superior to that of the basic iterative method in this paper we use the preconditioning matrix i s if a coefficient matrix a is an irreducibly diagonally dominant z matrix then i s a is also a strictly diagonally dominant z matrix it is shown that the proposed method is also superior to other iterative methods

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

the preconditioned gauss seidel method faster than the sor method in recent years a number of preconditioners have been applied to linear systems a d gunawardena s k jain l snyder modified iterative methods for consistent linear systems linear algebra appl 154 156 1991 123 143 t kohno h kotakemori h niki m usui improving modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x j comput appl math 145 2002 373 378 h kotakemori h niki n okamoto accelerated iteration method for z matrices j comput appl math 75 1996 87 97 m usui h niki t kohno adaptive gauss seidel method for linear systems internat j comput math 51 1994 119 125 10 since these preconditioners are constructed from the elements of the upper triangular part of the coefficient matrix the preconditioning effect is not observed on the nth row of matrix a in the present paper in order to deal with this drawback we propose a new preconditioner in addition the convergence and comparison theorems of the proposed method are established simple numerical examples are also given and we show that the convergence rate of the proposed method is better than that of the optimum sor

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

a note on the improving modified gauss seidel imgs method abstract in this paper we first provide another proof for a theorem given by sun l sun a comparison theorem for the sor iterative method j comput appl math 181 2005 336 341 by showing that spectral radius of the gauss seidel method is not greater than that of the sor method when 0 1 next convergence results of the imgs method for both an h matrix and a symmetric positive definite matrix are provided

theorems on m splittings of a singular m matrix which depend on graph structure abstract let a m ne r n n be a splitting we investigate the spectral properties of the iteration matrix m 1n by considering the relationships of the graphs of a m n and m 1n we call a splitting an m splitting if m is a nonsingular m matrix and n 0 for an m splitting of an irreducible z matrix a we prove that the circuit index of m 1n is the greatest common divisor of certain sets of integers associated with the circuits of a for m splittings of a reducible singular m matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting these results hold under somewhat weaker assumptions

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

on optimal improvements of classical iterative schemes for z matrices many researchers have considered preconditioners applied to linear systems whose matrix coefficient is a z or an m matrix that make the associated jacobi and gauss seidel methods converge asymptotically faster than the unpreconditioned ones such preconditioners are chosen so that they eliminate the off diagonal elements of the same column or the elements of the first upper diagonal milaszewicz laa 93 1987 161 170 gunawardena et al laa 154 156 1991 123 143 in this work we generalize the previous preconditioners to obtain optimal methods good jacobi and gauss seidel algorithms are given and preconditioners that eliminate more than one entry per row are also proposed and analyzed moreover the behavior of the above preconditioners to the krylov subspace methods is studied

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

convergence analysis of the preconditioned gauss seidel method for h matrices in 1997 kohno et al toshiyuki kohno hisashi kotakemori hiroshi niki improving the modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 proved that the convergence rate of the preconditioned gauss seidel method for irreducibly diagonally dominant z matrices with a preconditioner i s a is superior to that of the basic iterative method in this paper we present a new preconditioner i k b which is different from the preconditioner given by kohno et al toshiyuki kohno hisashi kotakemori hiroshi niki improving the modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an h matrix meanwhile two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given

a note on the preconditioned gauss seidal gs method for linear systems in this note recent comparison results for preconditioned gauss seidel gs methods are discussed a new strict comparison result between two different preconditioned gs methods is given some errors in a recent article by niki et al j comput appl math 164 165 2004 587 are pointed out and a new proof for the corresponding results in niki et al is presented

an analysis of thep version of the finite element method for nearly incompressible materials in this paper we analyze the behavior of the so calledp version of the finite element method when applied to the equations of plane strain linear elasticity we establish optimal rate error estimates that are uniformly valid independent of the value of the poisson ratio v in the interval 0 1 2 this shows that thep versiondoes not exhibit the degeneracy phenomenon which has led to the use of various only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material

modified gauss seidel type methods and jacobi type methods for z matrices abstract in this paper we present the convergence analysis for some modified gauss seidel and jacobi type iterative methods and provide a comparison of spectral radius among the gauss seidel iterative method and these modified methods some recent results are improved

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

the survey of preconditioners used for accelerating the rate of convergence in the gauss seidel method several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the gauss seidel method in this article on the basis of nonnegative matrix comparisons between some splittings for such preconditioned matrices are derived simple numerical examples are also given

convergence analysis of the two preconditioned iterative methods for m matrix linear systems in this paper we present the two preconditioners i s and i s r for solving m matrix linear systems and discuss the convergence of the two preconditioned iterative methods meanwhile we obtain comparison theorems between the two preconditioned iterative methods and consider the solution of m matrix linear systems by preconditioned krylov subspace methods numerical experiments are given to validate the performance of the preconditioners