a continuous framework for feti dp with a mesh independent condition number for the dual problem abstract we present an abstract setting for a variation of the feti dp method applied to second order elliptic problems in this setting the matrix iteration for the dual problem has a mesh independent condition number this work improves the ideas recently introduced by bernardi et al c bernardi t chacon rebollo e chacon vera a feti method with a mesh independent condition number for the iteration matrix comput methods appl mech engrg 197 13 16 2008 1410 1429 the continuity restrictions for the displacement field across interfaces are weakly imposed using the natural trace norm instead of pointwise continuity although a slight coupling between subdomains is introduced still a parallel computation is possible some numerical tests are also performed to illustrate the method

approximate factorization constraint preconditioners for saddle point matrices we consider the application of the conjugate gradient method to the solution of large symmetric indefinite linear systems special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given numerical experiments validate these conclusions

permutation modules over table algebras and applications to association schemes abstract inspired by the notion of an action of a finite hypergroup on a finite set we introduce the more general concept of a permutation module over a table algebra it is easy to see that each permutation module over a table algebra is a direct sum of transitive permutation modules among the transitive permutation modules the w maximal and the maximal permutation modules are the most interesting ones we give various characterizations of these modules and we shall see that a standard table algebra admits a maximal transitive permutation module if and only if it arises from a finite association scheme we also show that the regular module of a standard table algebra is isomorphic to a direct summand of each w maximal transitive permutation module as a consequence one obtains 1 m for any irreducible character of the bose mesner algebra of a finite association scheme and its multiplicity m

semi convergence of parameterized uzawa waveform relaxation method for a class of differential algebraic equations in this paper we propose an efficient parameterized uzawa waveform relaxation method for solving a class of initial value problems of differential algebraic equations daes the semi convergence of this method is studied furthermore the optimal iteration parameters and the corresponding optimal factor for the parameterized uzawa waveform relaxation method are determined two numerical examples are given to illustrate the theoretical results

a relaxed deteriorated pss preconditioner for nonsymmetric saddle point problems from the steady navier stokes equation for nonsymmetric saddle point problems arising from the steady navier stokes equations pan ng and bai presented a deteriorated positive definite and skew hermitian splitting dpss preconditioner pan et al 2006 to accelerate the convergence rates of the krylov subspace iteration methods such as gmres in this paper the unconditional convergence property of the dpss iteration method is proved and a relaxed dpss rdpss preconditioner is proposed the rdpss preconditioner is much closer to the coefficient matrix than the dpss preconditioner in certain norm which straightforwardly results in an rdpss iteration method the convergence conditions of the rdpss iteration are analyzed and the optimal parameter which minimizes the spectral radius of the rdpss iteration matrix is derived using the rdpss preconditioner to accelerate some krylov subspace methods like gmres is also studied the eigenproperty of the preconditioned matrix is described and an upper bound of the degree of the minimal polynomial of the preconditioned matrix is obtained finally numerical experiments of a model navier stokes equation are presented to illustrate the efficiency of the rdpss preconditioner

character products of association schemes since group algebras of finite groups are hopf algebras products of characters of finite groups are characters too in the present paper we prove that products of characters of finite schemes g are characters if one of the two factors contains the thin residue of g in its kernel we also give details in this situation

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

a relaxed dimensional factorization preconditioner for the incompressible navier stokes equations in this paper we introduce a relaxed dimensional factorization rdf preconditioner for saddle point problems properties of the preconditioned matrix are analyzed and compared with those of the closely related dimensional splitting ds preconditioner recently introduced by benzi and guo 7 numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the rdf preconditioner with respect to both mesh size and viscosity

aor uzawa iterative method for a class of complex symmetric linear system of equations abstract in this paper based on accelerated overrelaxation aor method and uzawa method we present aor uzawa iterative method for solving a broad class of complex symmetric linear systems we investigate its convergence properties in addition the resulting aor uzawa preconditioner is used to precondition krylov subspace methods such as the restarted generalized minimal residual gmres method for solving the real equivalent formulation of the complex symmetric system finally two numerical examples are given to show the effectiveness of the proposed method

on structures of quasi thin table algebras and applications to association schemes abstract in this paper we develop a structure theory for a class of table algebras i e the so called quasi thin table algebras they are direct generalizations of quasi thin association schemes although this class of table algebras is rather close to finite groups its structural properties are quite different from those of finite groups the thin radical and thin residue give rise to two group structures for every table algebra they play the central role in our discussions applications to association schemes are also discussed and some new results about quasi thin association schemes are obtained in particular we will give necessary and sufficient conditions under which a commutative quasi thin association scheme has multiplicities 1 or 2 we will need these results in the study of the characterization and classification of double quasi thin association schemes in 22

on semi convergence of the generalized shift splitting iteration method for singular nonsymmetric saddle point problems recently a class of generalized shift splitting iteration methods were proposed for solving nonsingular nonsymmetric saddle point problems cao et al 2015 in this paper the generalized shift splitting iteration method is extended to solve singular nonsymmetric saddle point problems semi convergence of the generalized shift splitting iteration method is carefully analyzed which shows that the iterative sequence generated by the generalized shift splitting iteration method converges to a solution of the singular saddle point problem unconditionally numerical results verify the robustness and efficiency of the generalized shift splitting iteration method

adaptive wavelet methods for saddle point problems optimal convergence rates in this paper an adaptive wavelet scheme for saddle point problems is developed and analyzed under the assumption that the underlying continuous problem satisfies the inf sup condition it is shown in the first part under which circumstances the scheme exhibits asymptotically optimal complexity this means that within a certain range the convergence rate which relates the achieved accuracy to the number of involved degrees of freedom is asymptotically the same as the error of the best wavelet n term approximation of the solution with respect to the relevant norms moreover the computational work needed to compute the approximate solution stays proportional to the number of degrees of freedom it is remarkable that compatibility constraints on the trial spaces such as the ladyzhenskaya babuska brezzi lbb condition do not arise in the second part the general results are applied to the stokes problem aside from the verification of those requirements on the algorithmic ingredients the theoretical analysis had been based upon the regularity of the solutions in certain besov scales is analyzed these results reveal under which circumstances the work accuracy balance of the adaptive scheme is even asymptotically better than that resulting from preassigned uniform refinements this in turn is used to select and interpret some first numerical experiments that are to quantitatively complement the theoretical results for the stokes problem

an adaptive uzawa fem for the stokes problem convergence without the inf sup condition we introduce and study an adaptive finite element method fem for the stokes system based on an uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity we show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity whereas for pressure the elements can be either discontinuous of degree k 1 or continuous of degree k 1 and k the popular taylor hood family is the sole example of stable elements included in the theory which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf sup condition we discuss the realization and complexity of the elliptic adaptive inner solver and provide consistent computational evidence that the resulting meshes are quasi optimal

block triangular and skew hermitian splitting methods for positive definite linear systems by further generalizing the concept of hermitian or normal and skew hermitian splitting for a non hermitian and positive definite matrix we introduce a new splitting called positive definite and skew hermitian splitting pss and then establish a class of pss methods similar to the hermitian or normal and skew hermitian splitting hss or nss method for iteratively solving the positive definite systems of linear equations theoretical analysis shows that the pss method converges unconditionally to the exact solution of the linear system with the upper bound of its convergence factor dependent only on the spectrum of the positive definite splitting matrix and independent of the spectrum of the skew hermitian splitting matrix as well as the eigenvectors of all matrices involved when we specialize the pss to block triangular or triangular and skew hermitian splitting btss or tss the pss method naturally leads to a btss or tss iteration method which may be more practical and efficient than the hss and nss iteration methods applications of the btss method to the linear systems of block two by two structures are discussed in detail numerical experiments further show the effectiveness of our new methods

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

adaptive inexact iterative algorithms based on polynomial degree robust a posteriori estimates for the stokes problem in this paper we develop adaptive inexact versions of iterative algorithms applied to finite element discretizations of the linear stokes problem we base our developments on an equilibrated stress a posteriori error estimate distinguishing the different error components namely the discretization error component the inner algebraic solver error component and possibly the outer algebraic solver error component for algorithms of the uzawa type we prove that our estimate gives a guaranteed upper bound on the total error as well as a polynomial degree robust local efficiency and this on each step of the employed iterative algorithm our adaptive algorithms stop the iterations when the corresponding error components do not have a significant influence on the total error the developed framework covers all standard conforming and conforming stabilized finite element methods on simplicial and rectangular parallelepipeds meshes in two or three space dimensions and an arbitrary algebraic solver implementation into the freefem programming language is invoked and numerical examples showcase the performance of our a posteriori estimates and of the proposed adaptive strategies as example we choose here the unpreconditioned and preconditioned uzawa algorithm and the preconditioned minimum residual minres algorithm in combination with the taylor hood discretization

a note on the positive stable block triangular preconditioner for generalized saddle point problems abstract in this paper we give a sharp eigenvalue bound for the positive stable block triangular preconditioned matrix presented in a recent paper by cao z h cao positive stable block triangular preconditioners for symmetric saddle point problems appl numer math 57 2007 899 910 the intervals containing these eigenvalues of the preconditioned matrix remove the origin which is benefit for further study numerical experiments of a model stokes problem are presented to show the estimate and the effectiveness of the positive stable block triangular preconditioners

preconditioning techniques for a mixed stokes darcy model in porous media applications we study numerical methods for a mixed stokes darcy model in porous media applications the global model is composed of two different submodels in a fluid region and a porous media region coupled through a set of interface conditions the weak formulation of the coupled model is of a saddle point type the mixed finite element discretization applied to the saddle point problem leads to a coupled indefinite and nonsymmetric linear system of algebraic equations we apply the preconditioned gmres method to solve the discrete system and are particularly interested in efficient and effective decoupled preconditioning techniques several decoupled preconditioners are proposed theoretical analysis and numerical experiments show the effectiveness and efficiency of the preconditioners effects of physical parameters on the convergence performance are also investigated

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

irreducible characters of wreath products in reality based algebras and applications to association schemes abstract wreath products in reality based algebras are generalizations of wreath products of table algebras and generalized camina frobenius pairs of c algebras in this paper we present characterizations of the wreath product in a reality based algebra by its irreducible characters and by the size of the zero submatrix of its character table applications to finite groups table algebras and association schemes are also discussed in particular we will show that the wreath product of one class association schemes is characterized by the zeros in its first eigenmatrix

a feti method with a mesh independent condition number for the iteration matrix abstract we introduce a framework for feti methods using ideas from the decomposition via lagrange multipliers of h 0 1 derived by raviart thomas p a raviart j m thomas primal hybrid finite element methods for second order elliptic equations math comput 31 138 1977 391 413 and complemented with the detailed work on polygonal domains developed by grisvard p grisvard singularities in boundary value problems rech math appl 22 1992 we compute the action of the lagrange multipliers using the natural h 00 1 2 scalar product therefore no consistency error appears our analysis allows to deal with cross points and floating subdomains in a natural manner as a byproduct we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning this result improves the standard asymptotic bound for this condition number given by 1 log h h 2 where h and h are the characteristic subdomain size and element size respectively shown by mandel tezaur in j mandel r tezaur convergence of a substructuring method with lagrange multipliers numer math 73 1996 473 487 numerical results that confirm our theoretical analysis are presented

a modified dimensional split preconditioner for generalized saddle point problems abstract for large and sparse saddle point linear systems arising from 2d linearized navier stokes equations benzi and guo recently studied a dimensional split ds preconditioner appl numer math 61 2011 66 76 by further applying it to generalized saddle point problems in this paper we present a modified dimensional split mds preconditioner this new preconditioner is based on a splitting of the generalized saddle point matrix resulting in an unconditional convergent fixed point iteration the basic iteration is accelerated by a krylov subspace method like restarted gmres the implementation of the mds preconditioner is discussed and a similar case is also analyzed finally numerical experiments of a model navier stokes problem are presented to illustrate the effectiveness of the mds preconditioner

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

a unified approach for uzawa algorithms we present a unified approach in analyzing uzawa iterative algorithms for saddle point problems we study the classical uzawa method the augmented lagrangian method and two versions of inexact uzawa algorithms the target application is the stokes system but other saddle point systems e g arising from mortar methods or lagrange multipliers methods can benefit from our study we prove convergence of uzawa algorithms and find optimal rates of convergence in an abstract setting on finite or infinite dimensional hilbert spaces the results can be used to design multilevel or adaptive algorithms for solving saddle point problems the discrete spaces do not have to satisfy the lbb stability condition

tables and large sample distribution theory for censored data correlation statistics for testing normality abstract plotting order statistics versus some variant of the normal scores is a standard graphical technique for assessing the assumption of normality to obtain an objective evaluation of the normal assumption it is customary to calculate the correlation coefficient associated with this plot the shapiro francia statistic is the square of the correlation between the observed order statistics and the expected values of standard normal order statistics whereas the shapiro wilk statistic also involves the covariances of the standard normal order statistics in a wide variety of applications an investigation of the plausibility of the normal or lognormal model is needed when the observations on strength or life length are right censored the plotting procedure still applies if the observations are censored at a fixed order statistic or a fixed time here the corresponding distribution theory for some modified versions of the shapiro wilk correlation statistic is investigated because the asymptotic th

saddle point problems bott duffin inverses abstract splines and oblique projections abstract in this note we present links between several different areas in numerical analysis and operator theory more precisely we show that several saddle point problems are solvable in the presence of a property called compatibility between a positive operator and a closed subspace of a hilbert space and the same happens with certain abstract spline problems these notions are related to the generalized bott duffin inverse

a new relaxed pss preconditioner for nonsymmetric saddle point problems a new relaxed pss like iteration scheme for the nonsymmetric saddle point problem is proposed as a stationary iterative method the new variant is proved to converge unconditionally when used for preconditioning the preconditioner differs from the coefficient matrix only in the upper right components the theoretical analysis shows that the preconditioned matrix has a well clustered eigenvalues around 1 0 with a reasonable choice of the relaxation parameter this sound property is desirable in that the related krylov subspace method can converge much faster which is validated by numerical examples

a relaxed positive definite and skew hermitian splitting preconditioner for saddle point problems for saddle point linear system whose coefficient matrix is non hermitian of positive definite hermitian part pan et al 2006 proposed a positive definite and skew hermitian splitting pss preconditioner in this paper based on the pss preconditioner we present a relaxed positive definite and skew hermitian splitting rpss preconditioner we analyze the spectral properties of the new preconditioned matrix and conclude that the rpss preconditioner has much better properties than pss numerical experiments of a model navier stokes problem are presented to illustrate the effectiveness of the new preconditioner

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

residual reduction algorithms for nonsymmetric saddle point problems in this paper we introduce and analyze uzawa algorithms for non symmetric saddle point systems convergence for the algorithms is established based on new spectral results about schur complements a new uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework numerical results supporting the efficiency of the algorithms are presented for finite element discretization of steady state navier stokes equations

some structure theory of table algebras and applications to association schemes abstract in this paper we prove some basic structure theorems for arbitrary table algebras in particular we prove a krull schmidt theorem for arbitrary table algebras and give applications to association schemes

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

on the nonlinear inexact uzawa algorithm for saddle point problems this paper discusses convergence behavior of the nonlinear inexact uzawa algorithm for solving saddle point problems presented in a recent paper of bramble pasciak and vassilev siam j numer anal 34 1997 pp 1072 1092 it is shown that this algorithm converges under a condition weaker than that stated in their paper

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

a new method to introduce constraints in cell centered lagrangian schemes we describe a new method to introduce constraints in cell centered lagrangian schemes in the framework of compressible hydrodynamics in this paper we apply it to the modeling of contact and sliding on solid wall boundaries we illustrate our method which is based on the minimization of a specific objective function by several basic problems

new preconditioners for saddle point problems we present new preconditioners based on matrix splittings for the saddle point problems the spectral property of one of the preconditioned matrix is studied in detail numerical examples are used to illustrate the efficiency of the new preconditioners

computational scales of sobolev norms with application to preconditioning this paper provides a framework for developing computationally efficient multilevel preconditioners and representations for sobolev norms specifically given a hilbert space v and a nested sequence of subspaces v 1 c v 2 c c v we construct operators which are spectrally equivalent to those of the form a k k q k q k 1 here k k 1 2 are positive numbers and q k is the orthogonal projector onto v k with q 0 0 we first present abstract results which show when a is spectrally equivalent to a similarly constructed operator a defined in terms of an approximation q k of q k for k 1 2 we show that these results lead to efficient preconditioners for discretizations of differential and pscudo differential operators of positive and negative order these results extend to sums of operators for example singularly perturbed problems such as i e can be preconditioned uniformly independently of the parameter e we also show how to precondition an operator which results from tikhonov regularization of a problem with noisy data finally we describe how the technique provides computationally efficient bounded discrete extensions which have applications to domain decomposition

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

modeling activity times by the parkinson distribution with a lognormal core theory and validation abstract based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times however raw data on activity times are often subject to rounding and to the parkinson effect we address those factors in our statistical tests by using a generalized version of the parkinson distribution with random censoring of earliness ultimately validating our model with field data from several sources we also confirm that project activities exhibit stochastic dependence that can be modeled by linear association

the uzawa pps iteration methods for nonsingular and singular non hermitian saddle point problems abstract in this paper based on the positive definite and positive semidefinite splitting pps iteration scheme we establish a class of uzawa pps iteration methods for solving nonsingular and singular non hermitian saddle point problems with the 1 1 part of the coefficient matrix being non hermitian positive definite theoretical analyses show that the convergence and semi convergence properties of the proposed methods can be guaranteed under suitable conditions furthermore we consider acceleration of the uzawa pps methods by krylov subspace like gmres methods and discuss the spectral properties of the corresponding preconditioned matrix numerical experiments are given to confirm the theoretical results which show that the feasibility and effectiveness of the proposed methods and preconditioners