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

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

a multi parameters preconditioned aor iterative method for linear systems abstract in order to improve the convergence rates of iterative method solving the linear system ax b a preconditioned aor iterative method with a multi parameters preconditioner i s is proposed some convergence and comparison results for i 0 1 are given when a is an l matrix when a is an h matrix the convergence of the corresponding methods is discussed for i 0 i where i 1 furthermore effectiveness of the new preconditioner method is shown by numerical experiments numerical experiments show that our methods are superior to the basic aor iterative methods

exact analysis of level crossing statistics for d 1 dimensional fluctuating surfaces we carry out an exact analysis of the average frequency xi in the direction xi of positiveslope crossing of a given level such that h x t bar h of growing surfaces in spatial dimension d here h x t is the surface height at time t and bar h is its mean value we analyze the problem when the surface growth dynamics is governed by the kardar parisi zhang kpz equation without surface tension in the time regime prior to appearance of cusp singularities sharp valleys as well as in the random deposition rd model the total number n of such level crossings with positive slope in all the directions is then shown to scale with time as td 2 for both the kpz equation and the rd model

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

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

zero tension kardar parisi zhang equation in d 1 dimensions the joint probability distribution function pdf of the height and its gradients is derived for a zero tension d 1 dimensional kardar parisi zhang kpz equation it is proved that the height s pdf of zero tension kpz equation shows lack of positivity after a finite time t c the properties of zero tension kpz equation and its differences with the case that it possess an infinitesimal surface tension is discussed also potential relation between the time scale t c and the singularity time scale t c v 0 of the kpz equation with an infinitesimal surface tension is investigated

singularity time scale of the kardar parisi zhang equation in 2 1 dimensions a master equation for the kardar parisi zhang kpz equation in 2 1 dimensions is developed in the fully nonlinear regime we determine the finite time scale of the singularity formation in terms of the characteristics of forcing the exact probability density function of the one point height field is obtained correspondingly

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

global study of rayleigh duffing oscillators in this paper we investigate the global dynamics of rayleigh duffing oscillators with global parameters including equilibria at both finity and infinity existences and coexistence of limit cycles and homoclinic loops in fact this oscillator will occur hopf bifurcations homoclinic bifurcations and double limit cycle bifurcations moreover we find that the homoclinic bifurcation of this oscillator is special which is a gluing bifurcation the global bifurcation diagram and all phase portrait are given and numerical simulations are shown to verify our analysis finally

a comparison theorem of the improving gauss seidel method for h matrix and its comparison matrix in 1997 kohno et al have reported that the improving modified gauss seidel method which was referred to as the imgs method was superior to the classical iterative methods h matrix is a widely used matrix in this paper we apply this method to h matrix and its comparison matrix with a more general splitting we present the corresponding convergence results and the comparison results of the spectral radius the convergence rates are as well as compared some recent results are improved

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

turbulence without pressure we develop exact field theoretic methods to treat turbulence when the effect of pressure is negligible we find explicit forms of certain probability distributions demonstrate that the breakdown of galilean invariance is responsible for intermittency and establish the operator product expansion we also indicate how the effects of pressure can be turned on perturbatively

the generalized hss method for solving singular linear systems for the singular non hermitian and positive semidefinite linear systems we propose an alternating direction iterative method with two parameters based on the hermitian and skew hermitian splitting the semi convergence analysis and the quasi optimal parameters of the proposed method are discussed moreover the corresponding preconditioner based on the splitting is given to improve the semi convergence rate of the gmres method numerical examples are given to illustrate the theoretical results and the efficiency of the generalized hss method either as a solver or a preconditioner for gmres

on upper triangular block weak regular splittings of a singular m matrix abstract let a be in the frobenius normal form and let a m n be a weak regular splitting we call this weak regular splitting an upper triangular block weak regular splitting if m and n are upper triangular block matrices partitioned in the same way as a first we study weak regular splittings of a singular irreducible m matrix and obtain some interesting results we also investigate the index of the spectral radius of the iteration matrix m 1 n when the splitting a m n is assumed to be upper triangular weak regular and we obtain ind 1 m 1 n ind 0 a by this result we improve the main results obtained by h schneider

two sided bounds for the inverse of an h matrix abstract the paper presents a simple characterization of a real h matrix and two sided componentwise bounds for its inverse in terms of the comparison matrix and the so called z and positive parts these bounds improving the well known ostrowsky result are also extended to a larger class of matrices

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 surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

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 new iterative method for solving linear systems abstract a new iterative method for solving linear systems is derived it can be considered as a modification of the gauss seidel method the modified method can be two times faster than the original one

statistical theory for the kardar parisi zhang equation in 1 1 dimensions the kardar parisi zhang kpz equation in 1 1 dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous we develop a statistical theory for the kpz equation in 1 1 dimensions driven with a random forcing that is white in time and gaussian correlated in space a master equation is derived for the joint probability density function of height difference and height gradient p h ensuremath overline h ensuremath partial x h t when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width in the time scales before the creation of the sharp valleys we find the exact generating function of h ensuremath overline h and ensuremath partial x h the time scale of the sharp valley formation is expressed in terms of the force characteristics in the stationary state when the sharp valleys are fully developed finite size corrections to the scaling laws of the structure functions h ensuremath overline h n ensuremath partial x h m are also obtained

comments on nonlinear dynamics of a non ideal duffing rayleigh oscillator numerical and analytical approaches an analytical and numerical investigation into the dynamic interaction between a cantilever beam with nonlinear damping and stiffness behavior modeled by the duffing rayleigh equation and a non ideal motor that is connected to the end of the beam is presented non stationary and steady state responses in the resonance region as well as the passage through resonance behavior when the frequency of the excitation is varied are analyzed the influences of nonlinear stiffness nonlinear damping and the extent of the unbalance in the motor are examined it is found that in this situation so called sommerfeld effects may be observed the increase required by a source operating near the resonance results in a small change in the frequency but there is a large increase in the amplitude of the resultant vibration and the jump phenomenon occurs

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

a general preconditioner for linear complementarity problem with an m matrix abstract in this paper we first present a general preconditioner p for solving linear complementarity problem lcp associated with an m matrix a and a vector f and prove that the lcp a f is equivalent to the lcp p a p f then based on this general preconditioner p two preconditioned ssor methods for solving the linear complementarity problems are proposed we show that this general preconditioner p accelerates the convergence of two ssor methods under the assumption that p a is a z matrix in addition we also give a practically concrete choice for the preconditioner p satisfying aforementioned assumption numerical examples are used to illustrate the theoretical results obtained

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

a preconditioned two step modulus based matrix splitting iteration method for linear complementarity problem abstract in this paper a preconditioned two step modulus based matrix splitting iteration method for linear complementarity problems associated with an m matrix is proposed the convergence analysis of the presented method is given in particular we provide a comparison theorem between preconditioned two step modulus based gauss seidel ptmgs iteration method and two step modulus based gauss seidel tmgs iteration method which shows that ptmgs method improves the convergence rate of original tmgs method for linear complementarity problem numerical tested examples are used to illustrate the theoretical analysis

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

experimental bifurcations and chaos in a modified self sustained macro electromechanical system abstract a class of self sustained macro electromechanical maems systems is made up of a rayleigh duffing oscillator actuating a mechanical arm through a magnetic coupling in this paper to avoid experimental constraints an audio amplifier is added to the device quenching phenomenon bifurcation and chaos are predicted and shown to occur in a device of this class of maems especially by using linear stability analysis the condition for the quenching phenomenon is derived chaos and bifurcation are predicted using lyapunov exponent and bifurcation diagram a prototype of device is designed and fabricated experimental results for this device that are consistent with results from theoretical investigations are presented and convincingly show quenching phenomenon bifurcation and chaos

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

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

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

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