comparison and stability of solutions to a class of quasilinear parabolic problems on presente des resultats de comparaison et d unicite pour les solutions de problemes aux valeurs limites quasilineaires paraboliques avec et sans obstacles un resultat de stabilite dans l 1 donne la stabilisation asymptotique dans cet espace quand t vers le probleme elliptique correspondant

block diagonal and constraint preconditioners for nonsymmetric indefinite linear systems part i theory we study block diagonal preconditioners and an efficient variant of constraint preconditioners for general two by two block linear systems with zero 2 2 block we derive block diagonal preconditioners from a splitting of the 1 1 block of the matrix from the resulting preconditioned system we derive a smaller so called related system that yields the solution of the original problem solving the related system corresponds to an efficient implementation of constraint preconditioning we analyze the properties of both classes of preconditioned matrices in particular their spectra using analytical results we show that the related system matrix has the more favorable spectrum which in many applications translates into faster convergence for krylov subspace methods we show that fast convergence depends mainly on the quality of the splitting a topic for which a substantial body of theory exists our analysis also provides a number of new relations between block diagonal preconditioners and constraint preconditioners for constrained problems solving the related system produces iterates that satisfy the constraints exactly just as for systems with a constraint preconditioner finally for the lagrange multiplier formulation of a constrained optimization problem we show how scaling nonlinear constraints can dramatically improve the convergence for linear systems in a newton iteration our theoretical results are confirmed by numerical experiments on a constrained optimization problem we consider the general nonsymmetric nonsingular case our only additional requirement is the nonsingularity of the schur complement type matrix derived from the splitting that defines the preconditioners in particular the 1 2 block need not equal the transposed 2 1 block and the 1 1 block might be indefinite or even singular this is the first paper in a two part sequence in the second paper we will study the use of our preconditioners in a variety of applications

a block product preconditioner for saddle point problems abstract in this paper a block product bp preconditioner is established for saddle point problems spectral properties of the bp preconditioned matrix are investigated a strategy for practical choice of quasi optimal parameter is given numerical results on saddle point linear systems arising from stokes problems and weighted least square problems show that the proposed bp preconditioner is more economic to implement within krylov subspace acceleration than some extensively studied preconditioners

analysis and control of differential inclusions with anti periodic conditions we deal with the optimal control of systems driven by differential inclusions with anti periodic conditions in banach spaces the operators in the differential inclusions describing the control system all depend on control variables by a solution of the control system we mean a trajectory control pair we first prove that for fixed control variables the set of solutions is non empty for the corresponding differential inclusion with anti periodic conditions we then show the functional topological properties of the set of solutions finally we investigate the existence of solutions to the optimal control problem these abstract results can be used to study optimal control systems of evolutionary hemi variational inequalities

solutions of cauchy and periodic problems for evolution inclusions with multi valued wλ0 pseudomonotone maps abstract we consider differential operator inclusions with w 0 pseudomonotone multi valued maps the problem of investigation of solutions of cauchy and periodic problems is solved by faedo galerkin fg method important a priori estimates are obtained some topological descriptions of the resolvent operators are made

a block alternating splitting iteration method for a class of block two by two complex linear systems optimization problems with partial differential equations as constraints arise widely in many areas of science and engineering in this paper we focus on solving a class of block two by two complex linear systems arising from the distributed optimal control with time periodic parabolic equations a new block alternating splitting bas iteration method is presented for solving the class of complex linear systems the convergence theory and the spectral properties of the bas iteration method are discussed numerical experiments are presented to illustrate the efficiency of the bas iteration as a solver as well as a preconditioner for krylov subspace methods

eventually and asymptotically positive semigroups on banach lattices abstract we develop a theory of eventually positive c 0 semigroups on banach lattices that is of semigroups for which for every positive initial value the solution of the corresponding cauchy problem becomes positive for large times we give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators complementing existing results on spaces of continuous functions this enables us to treat a range of new examples including the square of the laplacian with dirichlet boundary conditions the bi laplacian on l p spaces the dirichlet to neumann operator on l 2 and the laplacian with non local boundary conditions on l 2 within the one unified theory we also introduce and analyse a weaker notion of eventual positivity which we call asymptotic positivity where trajectories associated with positive initial data converge to the positive cone in the banach lattice as t this allows us to discuss further examples which do not fall within the above mentioned framework among them a network flow with non positive mass transition and a certain delay differential equation

on inexact preconditioners for nonsymmetric matrices inexact versions of the block triangular preconditioners for nonsymmetric matrices of block two by two structures in m f murphy g h golub and a j wathen siam j sci comput 21 2000 pp 1969 1972 and i c f ipsen siam j sci comput 23 2001 pp 1050 1051 are presented and the two preconditioners for symmetric block two by two matrices in c durazzi and v ruggiero numer linear algebra appl 10 2003 pp 673 688 are extended to general nonsymmetric matrices moreover we precisely describe the spectral properties of the preconditioned matrices and the finite step termination properties of the preconditioned krylov subspace iteration methods with an optimal or galerkin property with respect to these preconditioners several numerical examples are performed to illustrate the effectiveness of the proposed preconditioners

positivity for equations involving polyharmonic operators with dirichlet boundary conditions cranston fabes and zhao 26 5 established the uniform bound sup x y 2 x 6 y r g1 n x z g1 n z y dz g1 n x y m 1 1 where g1 n x y is the green function for the laplacian with dirichlet boundary conditions on a lipschitz domain rn with n 3 see 27 for n 2 this estimate was used in 23 and 18 to obtain positivity uniformly with respect to f 0 for noncooperative elliptic systems as

quasilinear elliptic inclusions of hemivariational type extremality and compactness of the solution set abstract we consider the dirichlet boundary value problem for an elliptic inclusion governed by a quasilinear elliptic operator of leray lions type and a multivalued term which is given by the difference of clarke s generalized gradient of some locally lipschitz function and the subdifferential of some convex function problems of this kind arise e g in mechanical models described by nonconvex and nonsmooth energy functionals that result from nonmonotone multivalued constitutive laws our main goal is to characterize the solution set of the problem under consideration in particular we are going to prove that the solution set possesses extremal elements with respect to the underlying natural partial ordering of functions and that the solution set is compact the main tools used in the proofs are abstract results on pseudomonotone operators truncation and special test function techniques zorn s lemma as well as tools from nonsmooth analysis

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

multiple solutions of quasilinear periodic parabolic inclusions abstract the existence of multiple solutions for a class of quasilinear periodic parabolic boundary value problems is proved our proof is based on the one hand on the sub supersolution method for general quasilinear periodic parabolic inclusions on the other hand it relies on the construction of non overlapping ordered intervals of sub supersolutions by the use of appropriately designed quasilinear elliptic problems and the maximum and anti maximum principles our approach also allows us to provide an elementary existence proof for semilinear periodic parabolic problems which have been studied otherwise by rather involved and elaborated abstract topological tools

sub super solution method for a class of higher order evolution hemivariational inequalities abstract in this paper we extend the extremality results for the variational inequality to a higher order evolution hemivariational inequality more precisely we give an existence theorem of solution for the higher order evolution hemivariational inequality by using the sub super solution method we prove the compactness of the solution set within an order interval formed by the sub solution and super solution we also show an existence theorem of the extremal solution for the higher order evolution hemivariational inequality under consideration

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities abstract in this paper we consider the problem of the existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator using regularized approximating and first eigenfunction methods and the surjectivity result we prove the existence of solutions for quasilinear parabolic hemivariational inequalities

boundary hemivariational inequality problems with doubly nonlinear operators in this paper we investigate a class of nonlinear boundary hemivariational inequality problems under suitable hypotheses the existence of solutions is established via rewriting these problems into a class of evolution inclusions and using the discretization method and the theory of pseudomonotone operators moreover the continuous dependence result of the solutions to the initial data is given

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

existence and regularity results for doubly nonlinear inclusions with nonmonotone perturbation abstract this paper deals with a class of nonlinear evolution inclusions arising from enthalpy formulation of heat conduction problems with phase change and nonmonotone source using time discretization technique and monotone operators theory we show the existence of weak solutions then we prove strong convergence of approximate solutions and lift regularity of the weak solutions under appropriate conditions moreover application to physical model described by hemivariational inequality is given

preconditioning of complex linear systems from the helmholtz equation abstract in this paper for solving a class of complex linear systems from the helmholtz equation efficiently a new splitting preconditioner is established and a real valued preconditioned iterative method is presented spectral properties of the preconditioned matrix are discussed and bound on the eigenvalues of the preconditioned matrix is given theorem which provides the dimension of the krylov subspace methods for the preconditioned iteration method is obtained the implementation of the preconditioned method is given and the optimal choice of the accelerated parameter is derived in particular a more practical way to choose the accelerated parameter is also proposed numerical experiments arising from the helmholtz equation are used to illustrate the performance of the preconditioner which show the effectiveness and robustness of the new preconditioned gmres method and demonstrate meshsize independent and wave number insensitive convergence behavior

an abstract form of maximum and anti maximum principles of hopf s type abstract we consider an abstract linear elliptic boundary value problem au u f 0 in a strongly ordered banach space x the resolvent i a 1 of the closed linear operator a x x is assumed to be strongly positive and compact for all 1 where 1 denotes the principal eigenvalue of a we prove that there exists a constant f 0 depending upon f x 0 such that u i a 1 f x holds for all 1 1 here x x x x 0 denotes the positive cone in x with the topological interior x we also present nearly sharp sufficient conditions for a guaranteeing independence of 0 from f i e i a 1 is strongly positive for all 1 1 in particular for an elliptic dirichlet boundary value problem or for a strictly cooperative system of such problems the strong maximum and boundary point principles for 1 yield an anti maximum principle of hopf s type for 1 1 depending upon f if 0 f l p n p f 0 in a bounded c 2 domain in r n then u u 0 on whenever 1 1

optimal control of feedback control systems governed by hemivariational inequalities this paper is mainly concerned with the feedback control systems governed by evolution hemivariational inequalities by using the properties of multimaps and clarke s subdifferential we formulate some sufficient conditions to guarantee the existence result of feasible pairs of the feedback control systems we also present an existence result of optimal control pairs for an optimal control problem we emphasize that our results cannot be obtained straightforwardly from the previous works

uniform anti maximum principles abstract consider a second or higher order elliptic partial differential equation a u u f on an open bounded domain of r n with homogeneous boundary conditions b u 0 if there exists a simple eigenvalue for which the corresponding eigenfunction is positive and satisfies appropriate boundary estimates then an anti maximum principle holds for positive f lp with p large enough there exists f 0 such that for 1 1 f the solution is negative and for 1 f 1 the solution is positive we give conditions such that this sign reversing property is uniform there is 0 such that for all positive f the solution u is negative for 1 1 and positive for 1 1 two classes of higher order boundary value problems that satisfy these conditions will be given

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

block triangular preconditioners for saddle point problems with a penalty term block triangular preconditioners for a class of saddle point problems with a penalty term are considered an important example is the mixed formulation of the pure displacement problem in linear elasticity it is shown that the spectrum of the preconditioned system is contained in a real positive interval and that the interval bounds can be made independent of the discretization and penalty parameters this fact is used to construct bounds of the convergence rate of the gmres method with respect to an energy norm numerical results are given for gmres and bi cgstab

on augmentation block triangular preconditioners for regularized saddle point problems two augmentation block triangular preconditioners were introduced by shen et al 2012 for the regularized saddle point problem however the spectral analysis of the preconditioner based on the augmentation of the 2 2 block was not throughly derived there in this short paper we give a detailed spectral analysis on this preconditioner a numerical example is employed to validate the efficiency of the presented theoretical results

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

decay of energy for second order boundary hemivariational inequalities with coercive damping abstract in this article we consider the asymptotic behavior of solutions to second order evolution inclusions with the boundary multivalued term u t a t u t b u t j t u t 0 and u t a t u t b u t j t u t 0 where a is a possibly nonlinear coercive and pseudomonotone operator b is linear continuous symmetric and coercive is the trace operator and j is a locally lipschitz integral functional with denoting the clarke generalized gradient taken with respect to the second variable for both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity we discuss assumptions and provide examples of multivalued laws that satisfy them

on the bang bang principle for nonlinear evolution hemivariational inequalities control systems abstract the purpose of this paper is to discuss the control systems of nonlinear evolution hemivariational inequalities and their bang bang principle in banach space at first we show that extremal trajectories are in fact dense in the trajectories of the original system with convexified feedback control second by using the density results the nonlinear and infinite dimensional versions of the bang bang principle for hemivariational inequalities control systems is derived in the end an example is provided to illustrate the application of the obtained theory

estimates for green function and poisson kernels of higher order dirichlet boundary value problems pointwise estimates are derived for the kernels associated to the polyharmonic dirichlet problem on bounded smooth domains as a consequence one obtains optimal weighted l p l q regularity estimates for weights involving the distance function

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

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

existence and controllability results for stochastic fractional evolution hemivariational inequalities in this paper we study a class of stochastic evolution hemivariational inequalities with fractional derivative the existence of mild solutions and controllability results are obtained by applying fractional calculation stochastic analysis techniques a fixed point theorem of multivalued maps and properties of generalized clarke subdifferential an example is included to show the applicability of our results

coexistence periodic solutions of a doubly nonlinear parabolic system with neumann boundary conditions abstract this paper is concerned with a competitive and cooperative mathematical model for two biological populations which dislike crowding diffuse slowly and live in a common territory under different kind of intra and inter specific interferences the model consists of a system of two doubly nonlinear parabolic equations with nonlocal terms and neumann boundary conditions based on the theory of the leray schauder degree we obtain the coexistence periodic solutions namely the existence of two non trivial non negative periodic solutions representing the densities of the two interacting populations under different intra and inter specific interferences on their natural growth rates

a shifted nested splitting iterative method with applications to ill posed problems and image restoration we present a shifted nested iterative method for solving systems of linear equations with a coefficient matrix that contains a dominant skew hermitian part this new scheme is practically the inner outer iterations which employs the cgnr method as inner iteration to approximate each outer iterate while each outer iteration is induced by a convergent splitting of the coefficient matrix convergence properties of the new scheme are studied in depth and possible choices of the shift parameter are discussed moreover an adapted version of the method is used for ill posed problems and image restoration at the last numerical examples are used to further examine the effectiveness and robustness of the new method

a class of generalized mixed variational hemivariational inequalities i existence and uniqueness results abstract we investigate a generalized lagrange multiplier system in a banach space called a mixed variational hemivariational inequality mvhvi for short which contains a hemivariational inequality and a variational inequality first we employ the minty technique and a monotonicity argument to establish an equivalence theorem which provides three different equivalent formulations of the inequality problem without compactness for one of operators in the problem a general existence theorem for mvhvi is proved by using the fan knaster kuratowski mazurkiewicz principle combined with methods of nonsmooth analysis furthermore we demonstrate several crucial properties of the solution set to mvhvi which include boundedness convexity weak closedness and continuity finally a uniqueness result with respect to the first component of the solution for the inequality problem is proved by using the ladyzhenskaya babuska brezzi lbb condition all results are obtained in a general functional framework in reflexive banach spaces

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

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

evolutionary variational hemivariational inequalities existence and comparison results we consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset our main goal is to systematically develop the method of sub supersolution on the basis of which we then prove existence comparison compactness and extremality results the obtained results are applied to a general obstacle problem we improve the corresponding results in the recent monograph s carl v k le d motreanu nonsmooth variational problems and their inequalities comparison principles and applications springer monogr math springer new york 2007

on inexact hermitian and skew hermitian splitting methods for non hermitian positive definite linear systems we study theoretical properties of two inexact hermitian skew hermitian splitting ihss iteration methods for the large sparse non hermitian positive definite system of linear equations in the inner iteration processes we employ the conjugate gradient cg method to solve the linear systems associated with the hermitian part and the lanczos or conjugate gradient for normal equations cgne method to solve the linear systems associated with the skew hermitian part respectively resulting in ihss cg lanczos and ihss cg cgne iteration methods correspondingly theoretical analyses show that both ihss cg lanczos and ihss cg cgne converge unconditionally to the exact solution of the non hermitian positive definite linear system moreover their contraction factors and asymptotic convergence rates are dominantly dependent on the spectrum of the hermitian part but are less dependent on the spectrum of the skew hermitian part and are independent of the eigenvectors of the matrices involved optimal choices of the inner iteration steps in the ihss cg lanczos and ihss cg cgne iterations are discussed in detail by considering both global convergence speed and overall computation workload and computational efficiencies of both inexact iterations are analyzed and compared deliberately

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

weighted toeplitz regularized least squares computation for image restoration the main aim of this paper is to develop a fast algorithm for solving weighted toeplitz regularized least squares problems arising from image restoration based on augmented system formulation we develop new hermitian and skew hermitian splitting hss preconditioners for solving such linear systems the advantage of the proposed preconditioner is that the blurring matrix weighting matrix and regularization matrix can be decoupled such that the resulting preconditioner is not expensive to use we show that for a preconditioned system that is derived from a saddle point structure of size m n times m n the preconditioned matrix has an eigenvalue at 1 with multiplicity n and the other m eigenvalues of the form 1 lambda with lambda 1 we also study how to choose the hss parameter to minimize the magnitude of lambda and therefore the krylov subspace method applied to solving the preconditioned system converges very quickly experimental results for image restoration problems are re

sharp estimates for iterated green functions optimal pointwise estimates from above and below are obtained for iterated poly harmonic green functions corresponding to zero dirichlet boundary conditions for second order elliptic operators these estimates hold true on bounded c 1 1 domains for higher order elliptic operators we have to restrict ourselves to the polyharmonic operator on balls we will also consider applications to noncooperatively coupled elliptic systems and to the lifetime of conditioned brownian motion

motivations and realizations of krylov subspace methods for large sparse linear systems we briefly introduce typical and important direct and iterative methods for solving systems of linear equations concretely describe their fundamental characteristics in viewpoints of both theory and applications and clearly clarify the substantial differences among these methods in particular the motivations of searching the solution of a linear system in a krylov subspace are described and the algorithmic realizations of the generalized minimal residual gmres method are shown and several classes of state of the art algebraic preconditioners are briefly reviewed all this is useful for correctly deeply and completely understanding the application scopes theoretical properties and numerical behaviors of these methods and is also helpful in designing new methods for solving systems of linear equations

quasi uniformity for the abstract neumann antimaximum principle and applications with a priori estimates abstract in this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form l i provided that 0 is an eigenvalue of l with associated constant eigenfunctions to this purpose we introduce a new notion of quasi uniform maximum principle named k uniform maximum principle it holds for belonging to certain neighborhoods of 0 depending on the fixed positive multiplier k 0 which selects the good class of right hand sides our approach is based on a l l p estimate for some related problems as an application we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under neumann boundary conditions

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

entailment systems for stably locally compact locales the category scfru of stably continuous frames and preframe homomorphisms preserving finite meets and directed joins is dual to the karoubi envelope of a category ent whose objects are sets and whose morphisms x y are upper closed relations between the finite powersets fx and fy composition of these morphisms is the cut composition of jung et al that interfaces disjunction in the codomains with conjunctions in the domains and thereby relates to their multi lingual sequent calculus thus stably locally compact locales are represented by entailment systems x in which a generalization of entailment relations is idempotent for cut composition some constructions on stably locally compact locales are represented in terms of entailment systems products duality and powerlocales relational converse provides ent with an involution and this gives a simple treatment of the duality of stably locally compact locales if a and b are stably continuous frames then the internal preframe hom a b is isomorphic to a b where a is the hofmann lawson dual for a stably locally compact locale x the lower powerlocale of x is shown to be the dual of the upper powerlocale of the dual of x

new variant of the hss iteration method for weighted toeplitz regularized least squares problems from image restoration abstract for fast solving weighted toeplitz least squares problems from image restoration ng and pan 2014 studied a new hermitian and skew hermitian splitting nhss preconditioner in this paper a generalization of the nhss preconditioner and the corresponding iterative method are presented convergence for the new iteration method is studied and optimal choice of the parameters is discussed bounds on the eigenvalues and the corresponding eigenvector distributions are proposed the degree of the minimal polynomial of the preconditioned matrix is obtained numerical experiments arising from image restoration are provided which show the proposed iteration method is effective and confirm our theoretical results are correct

periodic solutions for nonlinear differential inclusions with multivalued perturbations abstract in this paper the periodic solutions for nonlinear differential inclusion governed by convex subdifferential and different perturbations are studied it is firstly proved that the differential inclusion has unique periodic solution if the perturbation function is a single valued function then by schauder s fixed point theorem and kakutani s fixed point theorem we prove that the differential inclusion has at least a periodic solution when the perturbation function is an upper semicontinuous or lower semicontinuous multifunction moreover the existence of the extremal solution for the differential inclusion is also studied finally based on one sided lipschitz osl assumption we prove the related relaxation theorem

a representation of stably compact spaces and patch topology this note presents a concrete representation of stably compact spaces this is used to give a simple and predicative description of the patch topology of a stably compact space j pure appl algebra to appear

existence and comparison principles for general quasilinear variational hemivariational inequalities we consider quasilinear elliptic variational hemivariational inequalities involving convex lower semicontinuous and locally lipschitz functionals we provide a generalization of the fundamental notion of sub and supersolutions on the basis of which we then develop the sub supersolution method for variational hemivariational inequalities including existence comparison compactness and extremality results

on the relationship between compact regularity and gentzen s cut rule the patch topology on a stably compact space generalizing the lawson topology on a domain is a coreflection of stably compact spaces in compact regular spaces this paper investigates compact regularity and the patch coreflection in multilingual sequent calculus mls which can be regarded as a category of predicative representations of stably compact spaces an object of mls is a certain sort of generalization of the positive fragment of gentzen s sequent calculus we show that an object of mls represents a compact regular space if and only if every sequent arises as an instance of gentzen s cut rule with complete freedom to choose the placement of the cut formula the relationship between compact regularity and gentzen s cut rule is further explicated by the patch coreflection in mls the construction is a universal solution up to a certain equivalence of tokens to the problem of adding opposites to a logic i e tokens that obey gentzen s rules for negation in the spectral case this is equivalent to adding boolean complements the paper closes by considering the full subcategory of mls consisting of objects with opposites by taking contrapositives of sequents we obtain an anti involution on morphisms making this category equivalent to the freyd scedrov allegory of compact regular spaces and closed binary relations moreover the category of maps of this allegory is predicatively equivalent to the image of the patch functor

a generalization of the inexact parameterized uzawa methods for saddle point problems abstract for large sparse saddle point problems bai and wang recently studied a class of parameterized inexact uzawa methods see z z bai z q wang on paramaterized inexact uzawa methods for generalized saddle point problems linear algebra appl 428 2008 2900 2932 in this paper we generalize these methods and propose a class of generalized inexact parameterized iterative schemes for solving the saddle point problems we derive conditions for guaranteeing the convergence of these iterative methods with different choices of the parameter matrices the generalized iterative methods lead to a series of existing and new iterative methods including the classical uzawa method the inexact uzawa method the gsor method and the giaor method