on time integration of groundwater flow equations by spectral methods a study of the computational performance of the recently introduced spectral approach for the time integration of finite element flow equations is performed two reduction methods are presented and discussed one method relies on the classical modal decomposition wherein the leftmost eigenpairs of a generalized symmetric eigenvalue problem are evaluated one at a time by a cost effective orthogonal deflation technique the other uses a set of lanczos vectors for the coordinate transformation matrix and involves a recursive product between the inverse of the stiffness matrix and a vector an extensive analysis of the behavior of the two methods is made with a representative sample problem of subsurface flow solved over a regular and an irregular mesh the results show that the spectral approach cannot be competitive from a computational viewpoint with a more traditional time stepping or direct integration scheme e g the crank nicolson scheme the eigenvector technique is slow to converge and a large portion if not all of the flow modes need to be determined to accurately describe the desired solution the lanczos algorithm may converge faster in the lanczos vector space however its actual performance depends to a large extent on the initial guessed vector and is adversely influenced by the requirement to solve an equivalent steady state problem at each iteration it is concluded that for a robust and efficient finite element code of transient ground water flow direct integration methods are generally to be preferred

the h infty calculus and sums of closed operators we develop a very general operator valued functional calculus for operators with an h infty calculus we then apply this to the joint functional calculus of two sectorial operators when one has an h infty calculus using this we prove theorem of dore venni type on sums of sectorial operators and apply our results to the problem of l p maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of banach spaces are essential here in the final section we exploit the special banach space structure of l 1 spaces and c k spaces to obtain some more detailed results in this setting

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

interpolation of weighted and vector valued hardy spaces real and complex interpolation methods when applied to the couple hpo e0 wo hp el wl give what is expected if eo and e1 are quasi banach lattices of measurable functions satisfying certain mild conditions and if log wi powj l p1 e bmo wo w1 being weights on the unit circle the last condition is in fact necessary it is expected of course that the resulting spaces coincide with the subspaces of analytic functions in the corresponding interpolation spaces for the couple lpo eo wo lp e1 w1

minimal eigenvalue of large sparse matrices by an efficient reverse power conjugate gradient scheme in the assessment of the minimal eigenvalue of large sparse positive definite matrices the shift method easily fails to give successful results since its rate of convergence may prove unacceptably slow a very efficient alternative approach is provided by a double iterative scheme wherein external and internal iterations are performed by the reverse power and the modified conjugate gradients respectively the wider the spectral interval the greater the success of this technique whose efficiency in engineering practice therefore increases with the problem size n the results obtained with large 800 n 2200 space positive definite matrices arising from the finite element integration of flow and elasticity equations show that an accurate estimate of the minimal eigenvalue is achieved after very few 10 external iterations and a number of internal iterations of the order of n

holomorphic martingales and interpolation between hardy spaces the complex method a probabilistic proof is given to identify the complex interpolation space of h1 t and h t as hp t introduction in this note a soft propabilistic proof of p w jones s theorem on the complex interpolation space between h1 and hoc is given we shall work with n th varopoulos s space of holomorhpic martingales the observation presented in this article is that the use of a stopping time decomposition simplifies constructions of serguei v kislyakov and quanhua xu to obtain the following theorem the complex interpolation space th t h t 0 o 0 e 1 coincides with hp t provided that 1 1 03 p as is well known this result has been obtained by p w jones using l estimates to the a problem see j his work also contains the description of the real interpolation spaces for the couple hl h at about the same time jean bourgain obtained a marcinkiewicz type decomposition using completely different techniques see b1 recently in a series of papers jean bourgain b2 serguei kislyakov kl k2 k x gilles pisier p and quanhua xu xl x2 obtained deep results concerning real and complex interpolation methods between vector valued weighted hardy spaces of analytic functions s kislyakov s paper kl contains the following idea to approximate the characteristic function 1 1f1 2 by analytic functions on the circle t he starts a max l itl and then considers 1 a iha where h denotes the hilbert transform on t received by the editors august 11 1992 and in revised form february 1 1994 originally communicated to the proceedings of the ams by dale alspach 1991 mathematics subject classification primary 60g46 42b30

a trace minimization algorithm for the generalized eigenvalue problem an algorithm for computing a few of the smallest or largest eigenvalues and associated eigenvectors of the large sparse generalized eigenvalue problem ax lambda bx is presented the matrices a and b are assumed to be symmetric and haphazardly sparse with b being positive definite the problem is treated as one of constrained optimization and an inverse iteration is developed which requires the solution of linear algebraic systems only to the accuracy demanded by a given subspace the rate of convergence of the method is established and a technique for improving it is discussed numerical experiments and comparisons with other methods are presented

martingale transforms and complex uniform convexity les transformees de martingale et les operateurs integraux singuliers de calderon zygmund sont bornees comme des operateurs de l 2 l 1 dans l 2 l q quand 0 q 1 si y est un sous espace reflexif de l 1 alors l 1 y peut se renormer pour etre 2 complexe uniformement convexe on donne une nouvelle demonstration de la propriete de cotype 2 de l 1 h

accelerated simultaneous iterations for large finite element eigenproblems abstract an accelerated simultaneous iteration method is presented for the solution of the generalized eigenproblem ax bx where a and b are real sparse symmetric positive definite matrices the approach is well suited for the determination of the leftmost eigenpairs of problems with large size n the procedure relies on the optimization of the rayleigh quotient over a subspace of orthogonal vectors by a conjugate gradient technique effectively preconditioned with the pointwise incomplete cholesky factorization the method is applied to the evaluation of the smallest 15 eigenpairs of finite element models with size ranging between 150 and 2300 the numerical experiments show that while the simultaneous conjugate gradient scheme fails to converge the accelerated iterations yield accurate results in a number of steps which is much smaller than n the new approach does not require the a priori estimate of any empirical parameter and appears to be a robust reliable and efficient tool for the partial eigensolution of large finite element problems

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

block subspace projection preconditioned conjugate gradient method in modal structural analysis abstract this paper considers the preconditioned block conjugate gradient method for solving the algebraic generalized partial eigenvalue problem which arises when the finite element method is applied to dynamic analysis in structural and solid mechanics the focus is on the development of an algorithm that keeps constant the iterable subspace dimension independently of the number of eigenpairs required novelties in this approach include a preconditioning strategy based on block incomplete factorization of the shifted stiffness matrix and analysis of unremovable errors which accumulate with increasing numbers of eigenpairs

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

an improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices abstract an accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of the p p 20 leftmost eigenvalues and eigenvectors of finite element symmetric positive definite p d matrices of very large size the optimization is performed on the rayleigh quotient of the deflated matrices by the aid of a conjugate gradient cg scheme effectively preconditioned with the incomplete cholesky factorization no a priori estimate of acceleration parameters is required numerical experiments on large arbitrarily sparse problems taken from the engineering finite elements f e practice show a very fast convergence rate for any value of p within the explored interval and particularly so for the minimal eigenpair in this case the number of iterations needed to achieve an accurate solution may be as much as 2 orders of magnitude smaller than the problem size several results concerning the spectral behavior of the cg preconditioning matrices are also given and discussed

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

arithmeticity discreteness and volume we give an arithmetic criterion which is sufficient to imply the discreteness of various two generator subgroups of p sl 2 c we then examine certain two generator groups which arise as extremals in various geometric problems in the theory of kleinian groups in particular those encountered in efforts to determine the smallest co volume the margulis constant and the minimal distance between elliptic axes we establish the discreteness and arithmeticity of a number of these extremal groups the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple

solution of the partial eigenproblem by iterative methods a combined iterative method is formulated for the partial solution of the eigenproblem ax bx that arises from the application of the finite element method the method is a combination of the conjugate gradient cg method and the symmetric successive co ordinate overrelaxation sscor method both of these methods belong to the same family of iterative methods which retain their vectorial form and approach the solution by seeking stationary points of the rayleigh quotient the formulation consists in splitting a characteristic matrix into the sum of two matrices one of which corresponds to the sscor matrix and then accelerating the associated iteration using the cg the behaviour of the method is illustrated for five test cases and comparisons are made with other iterative methods the influence of the relaxation parameter on the computational efficiency of the methods is also studied

an orthogonal accelerated deflation technique for large symmetric eigenproblems abstract an improvement in accelerated conjugate gradient iterations is presented for the evaluation of several of the leftmost eigenpairs of large sparse symmetric positive definite matrices the approach relies on an orthogonal deflation procedure and is based on the subsequent preconditioned conjugate gradient optimization of rayleigh quotients over the restricted space orthogonal to the set of eigenvectors previously computed comparison with the accelerated simultaneous iterations performed over large finite element problems with size up to 4500 shows that storage requirement is significantly less and cpu times may be reduced by a factor of two or more

interpolation between hp spaces the complex method the corollary follows immediately from theorem 1 and fefferman s theorem see 111 that bmo is the dual space of h before proceeding to further results we make some comments on the history of theorem 1 unfortunately the theorem h lm e lp l p 1 0 has been folklore for many years and is stated e g in 2 221 this is due to a small but inopportune typographical error in 111 it is stated on page 157 of that paper that h lp lq l q 1 8 e p 1 p co

geodesic intersections in arithmetic hyperbolic 3 manifolds it was shown by chinburg and reid that there exist closed hyperbolic 3 manifolds in which all closed geodesics are simple subsequently basmajian and wolpert showed that almost all quasi fuchsian 3 manifolds have all closed geodesics simple and disjoint the natural conjecture arose that the chinburg reid examples also had disjoint geodesics here we show that this conjecture is both almost true they have no geodesics that intersect except at right angles and spectacularly false any pair of closed geodesics admits infinitely many closed geodesics which intersects both geodesics of the pair perpendicularly the latter statement is shown to be true for all closed arithmetic hyperbolic 3 manifolds section 0 introduction by a hyperbolic n manifold we shall mean a complete orientable n dimensional riemannian manifold all of whose sectional curvatures are 1 if m is a hyperbolic 3 manifold the universal cover of m can be identified with h the upper half space model of hyperbolic 3 space andm is realized ash for some a discrete torsionfree subgroup of isom h3 now isom h3 can be identified with psl 2 c which in turn is isomorphic to pgl 2 c and is called a kleinian group in the sequel we will only be interested in the case when m is closed in which case is referred to as cocompact of interest to us is the structure of the set of closed geodesics in closed hyperbolic 3 manifolds the motivation comes from the following a closed geodesic in a closed hyperbolic n manifold is simple if it has no self intersections and nonsimple otherwise in dimension 2 every closed hyperbolic manifold has a non simple closed geodesic however in dimension 3 the situation is much more complex many closed hyperbolic 3 manifolds contain immersions of totally geodesic surfaces and so there are non simple closed geodesics in jr examples were given of closed hyperbolic 3 manifolds containing a non simple closed geodesic but having no immersed totally geodesic surface however it was shown in cr that there exist closed hyperbolic 3 manifolds in which all closed geodesics are simple subsequently basmajian and wolpert bw showed that almost all 3 manifolds arising as the quotient of h 1991 mathematics subject classification primary 57m50 secondary 30f40

a numerical study of various algorithms related to the preconditioned conjugate gradient method we present the results of a numerical study of the preconditioned conjugate gradient algorithm the minimal residual algorithm the biconjugate gradient algorithm and the bi minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems the application of the methods to unsymmetric matrices is considered we emphasize the importance of a good preconditioning look at various methods including icgg n and incomplete block factorization and make some practical recommendations some of the folk lore surrounding the semi iterative methods is dispelled

hahn banach extension of multilinear forms and summability the aim of this paper is to investigate close relations between the validity of hahn banach extension theorems for multilinear forms on banach spaces and summability properties of sequences from these spaces a case of particular importance occurs when we consider banach spaces which have the property that every bilinear form extends to any superspace

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

a comparison of lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems in the present paper we analyse the computational performance of the lanczos method and a recent optimization technique for the calculation of the p p 40 leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic pdes the accelerated conjugate gradient method is used to minimize successive rayleigh quotients defined in deflated subspaces of decreasing size the pointwise lanczos scheme is employed in combination with both the cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive lanczos vectors the three algorithms are applied to five sample problems of varying size up to almost 5000 the numerical results show that the lanczos approach with cholesky triangularization is generally faster up to a factor of 5 for small to moderately large matrices while the optimization method is superior for large problems in terms of both storage requirement and cpu time in the large case the lanczos cholesky scheme may be very expensive to run even on modern quite powerful computers

strict singularity of volterra type operators on hardy spaces abstract in this paper we first characterize the boundedness and compactness of volterra type operator s g f z 0 z f g d z d defined on hardy spaces h p 0 p the spectrum of s g is also obtained then we prove that s g fixes an isomorphic copy of l p and an isomorphic copy of l 2 if the operator s g is not compact on h p 1 p in particular this implies that the strict singularity of the operator s g coincides with the compactness of the operator s g on h p at last we post an open question for further study