projected nonsymmetric algebraic riccati equations and refining estimates of invariant and deflating subspaces we consider the numerical solution of the projected nonsymmetric algebraic riccati equations or their associated sylvester equations via newton s method arising in the refinement of estimates of invariant or deflating subspaces for a large and sparse real matrix a or pencil a b the engine of the method is the inversion of the matrix p 2 p 2 a i n or p l 2 p l 2 a b for some orthonormal p 2 or p l 2 from r n n m making use of the structures in a or a b and the sherman morrison woodbury formula our algorithms are efficient under appropriate assumptions as shown in our error analysis and illustrated by numerical examples

refined iterative algorithms based on arnoldi s process for large unsymmetric eigenproblems abstract arnoldi s method has been popular for computing the small number of selected eigenvalues and the associated eigenvectors of large unsymmetric matrices however the approximate eigenvectors or ritz vectors obtained by arnoldi s method cannot be guaranteed to converge in theory even if the approximate eigenvalues or ritz values do in order to circumvent this potential danger a new strategy is proposed that computes refined approximate eigenvectors by small sized singular value decompositions it is shown that refined approximate eigenvectors converge to eigenvectors if ritz values do moreover the resulting refined algorithms converge more rapidly we report some numerical experiments and compare the refined algorithms with their counterparts the iterative arnoldi and arnoldi chebyshev algorithms the results show that the refined algorithms are considerably more efficient than their counterparts

a dynamic thick restarted semi refined able algorithm for computing a few selected eigentriplets of large nonsymmetric matrices able method can be used to compute eigentriplets of large scale nonsymmetric matrices however there is no guarantee for the ritz vectors obtained by this method to converge even if the subspace is good enough furthermore for the sake of storage limitation and amount of computations restarting techniques are often needed in order to deal with these problems we propose a dynamic thick restarted semi refined able algorithm sable in which we use semi refined ritz vectors to approximate the desired eigenvectors the relationship between the novel method and the classical one is given theoretical results show that the new method can circumvent the possible danger that exists in the standard one in some degree numerical experiments are made on real world problems and comparisons are drown on the thick restarted able algorithm table and the dynamic thick restarted semi refined able algorithm sable they show that the latter is often more powerful and attractive than its standard counterpart

a harmonic lanczos bidiagonalization method for computing interior singular triplets of large matrices abstract we propose a harmonic lanczos bidiagonalization method for computing some interior singular triplets of large matrices we prove that the approximate singular triplet is convergent if the norm of a certain rayleigh quotient matrix is uniformly bounded and the approximate singular values are well separated combining with the implicit restarting technique we develop an implicitly restarted harmonic lanczos bidiagonalization algorithm and suggest a strategy to select shifts numerical experiments show that one can use this algorithm to compute the interior singular triplets efficiently

bootstrap j tests of nonnested linear regression models the j test for nonnested regression models often overrejects very severely as an asymptotic test we provide a theoretical analysis which explains why and when it performs badly this analysis implies that except in certain extreme cases the j test will perform very well when bootstrapped using several methods to speed up the simulations we obtain extremely accurate monte carlo results on the finite sample performance of the bootstrapped j test these results fully support the predictions of our theoretical analysis even in contexts where the analysis is not strictly applicable

a simple test for regression specification with non nested alternatives abstract in this paper i introduce a simple test for the presence of the data generating process among several non nested alternatives the test is an extension of the classical j test for non nested regression models i also provide a bootstrap version of the test that avoids possible size distortions inherited from the j test

polynomial characterizations of the approximate eigenvectors by the refined arnoldi method and an implicitly restarted refined arnoldi algorithm abstract it is well known that a ritz vector obtained by the lanczos method and the arnoldi method can be characterized by an elegant explicit polynomial whose roots are just the other m 1 ritz values of the matrix a in question from the m dimensional krylov subspace involved analogous results hold for the recently developed harmonic lanczos and arnoldi methods and the roots of the corresponding polynomial are now the other m 1 harmonic ritz values of a from the same subspace in this paper we investigate a polynomial characterization of the refined arnoldi method proposed by the author in recent years we derive a polynomial characterization of the refined arnoldi method and apply the implicitly restarting scheme proposed by sorensen to the refined arnoldi method the roots of this polynomial are used as shifts called refined shifts within an implicitly restarted refined arnoldi algorithm the shifts are interpreted to have the same nature as the exact shifts used within the implicitly restarted arnoldi algorithm proposed by sorensen numerical experiments compare the use of refined shifts with exact shifts within an implicitly restarted arnoldi algorithm the results also show that implicitly restarting the refined arnoldi method is far superior to the saad s explicitly restarted scheme

tests for model specification in the presence of alternative hypotheses some further results abstract in davidson and mackinnon 1981 two of the present authors proposed a novel and very simple procedure for testing the specification of a nonlinear regression model against the evidence provided by a non nested alternative in this paper we extend their results in several directions first we relax a number of the assumptions of the previous paper we admit the possibility that the nonlinear regression functions may depend on lagged dependent variables and we do not require that the error terms be normally distributed second we show how the earlier procedure may straightforwardly be generalized to the case where the two non nested models involve different transformations of the dependent variable finally we propose a simple procedure for testing non nested linear regression models which have endogenous variables on the right hand side and have therefore been estimated by two stage least squares

quasi kernel polynomials and their use in non hermitian matrix iterations abstract some of the most efficient iterative algorithms for large sparse hermitian matrix computations are based on orthogonal or kernel polynomials for the case of non hermitian matrices methods based on orthogonal or kernel polynomials are less satisfactory in that the resulting algorithms involve long recurrences consequently it is usually too expensive to run the full algorithms and restarts are necessary a typical example is the generalized minimal residual method gmres for solving non hermitian linear systems where work and storage per iteration grow linearly with the iteration number recently two quasi minimal residual methods qmr for solving non hermitian linear systems have been proposed which unlike gmres are based on short recurrences and hence can be used as true iterative schemes without restarts in this paper the concept of quasi kernel polynomials is introduced some general theory for quasi kernel polynomials is developed such as recurrence relations and a characterization of roots of quasi kernel polynomials as generalized eigenvalues it is pointed out that the qmr approaches are based on two particular instances of quasi kernel polynomials also the use of quasi kernel polynomials for approximating eigenvalues or pseudospectra of large sparse non hermitian matrices is briefly discussed

a global harmonic arnoldi method for large non hermitian eigenproblems with an application to multiple eigenvalue problems the global arnoldi method can be used to compute exterior eigenpairs of a large non hermitian matrix a but it does not work well for interior eigenvalue problems based on the global arnoldi process that generates an f orthonormal basis of a matrix krylov subspace we propose a global harmonic arnoldi method for computing certain harmonic f ritz pairs that are used to approximate some interior eigenpairs we propose computing the f rayleigh quotients of the large non hermitian matrix with respect to harmonic f ritz vectors and taking them as new approximate eigenvalues they are better and more reliable than the harmonic f ritz values the global harmonic arnoldi method inherits convergence properties of the harmonic arnoldi method applied to a larger matrix whose distinct eigenvalues are the same as those of the original given matrix some properties of the harmonic f ritz vectors are presented as an application assuming that a is diagonalizable we show that the global harmonic arnoldi method is able to solve multiple eigenvalue problems both in theory and in practice to be practical we develop an implicitly restarted global harmonic arnoldi algorithm with certain harmonic f shifts suggested in particular this algorithm can be adaptively used to solve multiple eigenvalue problems numerical experiments show that the algorithm is efficient for the eigenproblem and is reliable for quite ill conditioned multiple eigenproblems

chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems abstract the present paper deals with the problem of computing a few of the eigenvalues with largest or smallest real parts of a large sparse nonsymmetric matrix we present a general acceleration technique based on chebyshev polynomials and discuss its practical application to arnoldi s method and the subspace iteration method the resulting algorithms are compared with the classical ones in a few experiments which exhibit a sharp superiority of the arnoldi chebyshev approach

an analysis of the rayleigh ritz method for approximating eigenspaces this paper concerns the rayleigh ritz method for computing an approximation to an eigenspace x of a general matrix a from a subspace w that contains an approximation to x the method produces a pair n x that purports to approximate a pair l x where x is a basis for x and ax xl in this paper we consider the convergence of n x as the sine e of the angle between x and w approaches zero it is shown that under a natural hypothesis called the uniform separation condition the ritz pairs n x converge to the eigenpair l x when one is concerned with eigenvalues and eigenvectors one can compute certain refined ritz vectors whose convergence is guaranteed even when the uniform separation condition is not satisfied an attractive feature of the analysis is that it does not assume that a has distinct eigenvalues or is diagonalizable

an introduction to potential theory in calibrated geometry in this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry these functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties moreover they exist in abundance whereas the corresponding pluriharmonics are generally quite scarce a number of the results established in complex analysis via plurisubharmonic functions are extended to calibrated manifolds this paper introduces and investigates questions of pseudo convexity in the context of a general calibrated manifold x phi analogues of totally real submanifolds are introduced and used to construct enormous families of strictly phi convex spaces with every topological type allowed by morse theory specific calibrations are used as examples throughout in a sequel the duality between phi pluri sub harmonic functions and phi positive currents is investigated this study involves boundaries generalized jensen measures and other geometric objects on a calibrated manifold

approximation accuracy of the krylov subspaces for linear discrete ill posed problems abstract for the large scale linear discrete ill posed problem min a x b or a x b with b contaminated by gaussian white noise the lanczos bidiagonalization based krylov solver lsqr and its mathematically equivalent cgls the conjugate gradient cg method implicitly applied to a t a x a t b are most commonly used and cgme the cg method applied to min a a t y b or a a t y b with x a t y and lsmr which is equivalent to the minimal residual minres method applied to a t a x a t b have also been choices these methods exhibit typical semi convergence feature and the iteration number k plays the role of the regularization parameter however there has been no definitive answer to the long standing fundamental question can lsqr and cgls find 2 norm filtering best possible regularized solutions the same question is for cgme and lsmr too at iteration k lsqr cgme and lsmr compute different iterates from the same k dimensional krylov subspace a first and fundamental step towards answering the above question is to accurately estimate the accuracy of the underlying k dimensional krylov subspace approximating the k dimensional dominant right singular subspace of a assuming that the singular values of a are simple we present a general sin theorem for the 2 norm distances between these two subspaces and derive accurate estimates on them for severely moderately and mildly ill posed problems we also establish some relationships between the smallest ritz values and these distances numerical experiments justify the sharpness of our results

large scale complex eigenvalue problems abstract the nonsymmetric eigenvalue problem ax bx is discussed with special emphasis on linear algebra theory on algorithms implemented for solving large scale systems and on interpreting complex spectra obtained in applications from physics and engineering present day supercomputers make the required matrix computations feasible especially in view of the increase in memory

natural convection in steady solidification finite element analysis of a two phase rayleigh benard problem abstract galerkin finite element approximations and newton s method for solving free boundary problems are combined with computer implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt the newton method gives rapid convergence to steady state velocity temperature and pressure fields and melt solid interface shapes and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability the power of this combination is demonstrated for a two phase rayleigh benard problem composed of melt and and solid in a vertical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt solid interface is always a solution multiple cellular flows bifurcating from the static state are detected and followed as rayleigh number is varied changing the boundary conditions to approach those appropriate for the vertical bridgman solidification system causes imperfections that eliminate the static state the flow structure in the bridgman system is related to those for the rayleigh benard system by a continuous evolution of the boundary conditions

a block arnoldi chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices in this paper we describe a block version of arnoldi s method for computing a few eigenvalues with largest or smallest real parts the method is accelerated via chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum a parallel implementation of this method is investigated on the eight processor alliant fx 80 numerical results and comparisons with simultaneous iteration on some harwell boeing matrices are reported

cohomology of q convex spaces in top degrees it is shown that every strongly q complete subvariety of a complex analytic space has a fundamental system of strongly q complete neighborhoods as a consequence we find a simple proof of ohsawa s result that every non compact irreducible n dimensional analytic space is strongly n complete finally it is shown that l cohomology theory readily implies ohsawa s hodge decomposition and lefschetz isomorphism theorems for absolutely q convex manifolds

generalized block lanczos methods for large unsymmetric eigenproblems generalized block lanczos methods for large unsymmetric eigenproblems are presented which contain the block arnoldi method and the block arnoldi algorithms are developed the convergence of this class of methods is analyzed when the matrix a is diagonalizable upper bounds for the distances between normalized eigenvectors and a block krylov subspace are derived and a priori theoretical error bounds for ritz elements are established compared with generalized lanczos methods which contain arnoldi s method the convergence analysis shows that the block versions have two advantages first they may be efficient for computing clustered eigenvalues second they are able to solve multiple eigenproblems however a deep analysis exposes that the approximate eigenvectors or ritz vectors obtained by general orthogonal projection methods including generalized block methods may fail to converge theoretically for a general unsymmetric matrix a even if corresponding approximate eigenvalues or ritz values do since the convergence of ritz vectors needs more sufficient conditions which may be impossible to satisfy theoretically than that of ritz values does the issues of how to restart and to solve multiple eigenproblems are addressed and some numerical examples are reported to confirm the theoretical analysis

an implicitly restarted lanczos bidiagonalization method with refined harmonic shifts for computing smallest singular triplets e kokiopoulou et al developed an implicitly restarted lanczos bidiagonalization method named irlanb for computing the smallest singular triplets they use the wanted harmonic ritz values and the corresponding refined harmonic ritz vectors to approximate the desired smallest singular triplets however they use the unwanted harmonic ritz values as shifts named the harmonic shifts to implicitly restart their algorithm therefore although they replace the harmonic ritz vectors by the refined harmonic ritz vectors which are always better than the harmonic ritz vectors to improve the convergence of irlanb the subspace after implicitly restarting is the same as that without this replacement in this paper using the information of the refined harmonic ritz vectors we present a new shift strategy named the refined harmonic shifts to replace the harmonic shifts used in irlanb and obtain a new method called irrlanb the refined harmonic shifts are better than the harmonic shifts and can be computed cheaply and reliably the numerical experiments are reported to indicate that irrlanb is superior than irlanb

block arnoldi and davidson methods for unsymmetric large eigenvalue problems we present two methods for computing the leading eigenpairs of large sparse unsymmetric matrices namely the block arnoldi method and an adaptation of the davidson method to unsymmetric matrices we give some theoretical results concerning the convergence and discuss implementation aspects of the two methods finally some results of numerical tests on a variety of matrices in which we compare these two methods are reported

on the use of harmonic ritz pairs in approximating internal eigenpairs the goal of this paper is to increase our understanding of harmonic rayleigh ritz for real symmetric matrices we do this by discussing different though related topics a priori error analysis a posteriori error analysis a comparison with refined rayleigh ritz and the selection of a suitable harmonic ritz vector

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

deflated block krylov subspace methods for large scale eigenvalue problems we discuss a class of deflated block krylov subspace methods for solving large scale matrix eigenvalue problems the efficiency of an arnoldi type method is examined in computing partial or closely clustered eigenvalues of large matrices as an improvement we also propose a refined variant of the arnoldi type method comparisons show that the refined variant can further improve the arnoldi type method and both methods exhibit very regular convergence behavior

the convergence of harmonic ritz values harmonic ritz vectors and refined harmonic ritz vectors this paper concerns a harmonic projection method for computing an approximation to an eigenpair x of a large matrix a given a target point r and a subspace w that contains an approximation to x the harmonic projection method returns an approximation x to x three convergence results are established as the deviation e of x from w approaches zero first the harmonic ritz value r converges to a if a certain rayleigh quotient matrix is uniformly nonsingular second the harmonic ritz vector x converges to x if the rayleigh quotient matrix is uniformly nonsingular and remains well separated from the other harmonic ritz values third better error bounds for the convergence of are derived when x converges however we show that the harmonic projection method can fail to find the desired eigenvalue in other words the method can miss if it is very close to r to this end we propose to compute the rayleigh quotient p of a with respect to x and take it as a new approximate eigenvalue p is shown to converge to once x tends to x no matter how r is close to finally we show that if the rayleigh quotient matrix is uniformly nonsingular then the refined harmonic ritz vector or more generally the refined eigenvector approximation introduced by the author converges we construct examples to illustrate our theory

a new shift strategy for the implicitly restarted refined harmonic lanczos method abstract the implicitly restarted refined harmonic lanczos method is widely used for computing the interior eigenpairs of large real symmetric matrices in each restart it takes the wanted refined harmonic ritz pairs to be the approximate eigenpairs and takes the refined harmonic shifts to implicitly restart the algorithm in this paper we modify this method by replacing the refined harmonic shifts by new shifts based on a special direct sum decomposition of the projected subspace we build a new subspace in each restart and then take the harmonic ritz values onto it to be the new shifts the new shifts can be obtained from a small generalized eigenvalue problem and the computational cost is negligible numerical experiments show that the new shifts are generally better than the refined harmonic shifts

duality of positive currents and plurisubharmonic functions in calibrated geometry recently the authors showed that there is a robust potential theory attached to any calibrated manifold x phi in particular on x there exist phi plurisubharmonic functions phi convex domains phi convex boundaries etc all inter related and having a number of good properties in this paper we show that in a strong sense the plurisubharmonic functions are the polar duals of the phi submanifolds or more generally the phi currents studied in the original paper on calibrations in particular we establish an analogue of duval sibony duality which characterizes points in the phi convex hull of a compact set k subset x in terms of phi positive green s currents on x and jensen measures on k we also characterize boundaries of phi currents entirely in terms of phi plurisubharmonic functions specific calibrations are used as examples throughout analogues of the hodge conjecture in calibrated geometry are considered

tests of non nested regression models some results on small sample behaviour and the bootstrap the most popular procedures for testing a regression model against a single non nested alternative can be substantially oversized in small samples also when a regression model is to be tested in the presence of several non nested alternatives the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes this approach leads to an implicit overall test with a significance level that is not known even asymptotically it is shown that the bootstrap can be used to control significance levels in both types of situation power estimates for various tests using bootstrap critical values are also obtained and compared

the rayleigh ritz method refinement and arnoldi process for periodic matrix pairs we extend the rayleigh ritz method to the eigen problem of periodic matrix pairs assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero we show that there exist periodic ritz values that converge to the desired periodic eigenvalues unconditionally yet the periodic ritz vectors may fail to converge to overcome this potential problem we minimize residuals formed with periodic ritz values to produce the refined periodic ritz vectors which converge under the same assumption these results generalize the corresponding well known ones for rayleigh ritz approximations and their refinement for non periodic eigen problems in addition we consider a periodic arnoldi process which is particularly efficient when coupled with the rayleigh ritz method with refinement the numerical results illustrate that the refinement procedure produces excellent approximations to the original periodic eigenvectors

mixed hessian inequalities and uniqueness in the class mathcal e x omega m we prove a general inequality for mixed hessian measures by global arguments our method also yields a simplification for the case of complex monge ampere equation exploiting this and using kolodziej s mass concentration technique we also prove the uniqueness of the solutions to the complex hessian equation on compact kahler manifolds in the case of probability measures vanishing on formula presented polar sets

tchebychev acceleration technique for large scale nonsymmetric matrices the acceleration by tchebychev iteration for solving nonsymmetric eigenvalue problems is dicussed a simple algorithm is derived to obtain the optimal ellipse which passes through two eigenvalues in a complex plane relative to a reference complex eigenvalue new criteria are established to identify the optimal ellipse of the eigenspectrum the algorithm is fast reliable and does not require a search for all possible ellipses which enclose the spectrum the procedure is applicable to nonsymmetric linear systems as well

plurisubharmonic functions in calibrated geometry and q convexity let m be a kahler manifold an integrable function varphi on m is called q plurisubharmonic if the current dd c varphi wedge omega q 1 is positive we prove that varphi is q plurisubharmonic if and only if varphi is subharmonic on all q dimensional complex subvarieties we prove that a q plurisubharmonic function is q convex and admits a local approximation by smooth q plurisubharmonic functions for any closed subvariety z subset m dim mathbb c z leq q 1 there exists a strictly q plurisubharmonic function in a neighbourhood of z this result is known for q convex functions this theorem is used to give a new proof of sibony s lemma on integrability of positive closed p p forms which are integrable outside of a complex subvariety of codimension p 1

computing green currents via the heat kernel let x be a compact kahler manifold for an analytic cycle y x of complex codimension k the poincare duality assigns a class in the de rham cohomology which can be represented by a harmonic k k form y a green current gy connects both objects by the equality ddgy y y thus we can reconstruct y and its harmonic projection y from this equation because y is the locus where ddgy is not smooth while y is determined by its values on the dense open set x y furthermore the above equality tells us that y and y differ only by some exact current green currents for varieties of arbitrary dimension were systematically developed by h gillet and c soule in 3 these currents play a central role in arakelov theory see 10 and 7 on the one hand the existence of green currents follows more or less formally from the hodge decomposition for currents to do intersection theory on the other hand we need currents which behave well green forms and green currents of logarithmic type are examples of these currents see 2 and 3 here we present a method to find a canonical green current gy which depends only on the kahler manifold x and the cycle y this current gy is given by k k forms with l coefficients which are smooth on x y we start with repeating some basic results on kahler manifolds in 1 which can be found in the textbooks 5 or 11 furthermore we recall the main properties of the heat kernel before we consider the heat flow of dirac currents in section 2 obtaining a green operator for these currents in 3 we define the canonical harmonic green current and show that its harmonic projection is zero in section 4 we apply the heat kernel to intersections of properly intersecting cycles this is needed to derive a formula for the product of green currents in 5 however we have to restrict to cycles that intersect properly hence our results are weaker than those of 3 as we used a different approach we decided to present them here in section 6 we give examples which we found by a good guess 6 1 or because we know all eigen functions of the laplace operator 6 2 or from the explicit formula of the heat kernel 6 3 the last example shows how our techniques can be extended to non compact kahler manifolds for which a heat kernel exists we conclude in section 7 with some questions and remarks acknowledgment the author wishes to thank w gubler j kramer and u kuhn for many discussions which contributed to this paper the comments of the referee helped to clarify the exposition

harmonic and refined harmonic shift invert residual arnoldi and jacobi davidson methods for interior eigenvalue problems this paper concerns the harmonic shift invert residual arnoldi hsira and jacobi davidson hjd methods as well as their refined variants rhsira and rhjd for the interior eigenvalue problem each method needs to solve an inner linear system to expand the subspace successively when the linear systems are solved only approximately we are led to the inexact methods we prove that the inexact hsira rhsira hjd and rhjd methods mimic their exact counterparts well when the inner linear systems are solved with only low or modest accuracy we show that i the exact hsira and hjd expand subspaces better than the exact sira and jd and ii the exact rhsira and rhjd expand subspaces better than the exact hsira and hjd based on the theory we design stopping criteria for inner solves to be practical we present restarted hsira hjd rhsira and rhjd algorithms numerical results demonstrate that these algorithms are much more efficient than the restarted standard sira and jd algorithms and furthermore the refined harmonic algorithms outperform the harmonic ones very substantially

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

a refined harmonic lanczos bidiagonalization method and an implicitly restarted algorithm for computing the smallest singular triplets of large matrices the harmonic lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix a we prove that for good enough projection subspaces harmonic ritz values converge if the columns of a are strongly linearly independent on the other hand harmonic ritz values may miss some desired singular values when the columns of a are almost linearly dependent furthermore harmonic ritz vectors may converge irregularly and may even fail to converge based on the refined projection principle for large matrix eigenproblems due to the first author we propose a refined harmonic lanczos bidiagonalization method that takes the rayleigh quotients of the harmonic ritz vectors as approximate singular values and extracts the best approximate singular vectors called the refined harmonic ritz approximations from the given subspaces in the sense of residual minimizations the refined approximations are shown to converge to the desired singular vectors once the subspaces are sufficiently good and the rayleigh quotients converge an implicitly restarted refined harmonic lanczos bidiagonalization algorithm irrhlb is developed we study how to select the best possible shifts and suggest refined harmonic shifts that are theoretically better than the harmonic shifts used within the implicitly restarted harmonic lanczos bidiagonalization algorithm irhlb we propose a novel procedure that can numerically compute the refined harmonic shifts efficiently and accurately numerical experiments are reported that compare irrhlb with five other algorithms based on the lanczos bidiagonalization process it appears that irrhlb is at least competitive with them and can be considerably more efficient when computing the smallest singular triplets

a thick restarted block arnoldi algorithm with modified ritz vectors for large eigenproblems the block arnoldi method is one of the most commonly used techniques for large eigenproblems in this paper we exploit certain modified ritz vectors to take the place of ritz vectors in the thick restarted block arnoldi algorithm and propose a modified thick restarted block arnoldi algorithm for large eigenproblems we then consider how to periodically combine the refined subspace iterative method with the modified thick restarting block arnoldi algorithm for computing a few dominant eigenpairs of a large matrix the resulting algorithm is called a subspace block arnoldi algorithm numerical experiments show the efficiency of our new algorithms

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

a modified harmonic block arnoldi algorithm with adaptive shifts for large interior eigenproblems the harmonic block arnoldi method can be used to find interior eigenpairs of large matrices given a target point or shift t to which the needed interior eigenvalues are close the desired interior eigenpairs are the eigenvalues nearest t and the associated eigenvectors however it has been shown that the harmonic ritz vectors may converge erratically and even may fail to do so to do a better job a modified harmonic block arnoldi method is coined that replaces the harmonic ritz vectors by some modified harmonic ritz vectors the relationships between the modified harmonic block arnoldi method and the original one are analyzed moreover how to adaptively adjust shifts during iterations so as to improve convergence is also discussed numerical results on the efficiency of the new algorithm are reported

the distance of an eigenvector to a krylov subspace and the convergence of the arnoldi method for eigenvalue problems abstract we study the distance of an eigenvector of a diagonalizable matrix a to the krylov subspace generated from a and a given starting vector v this distance is involved in studies of the convergence of the arnoldi method for computing eigenvalues contrary to the previous studies on this problem we provide closed form expressions for this distance in terms of the eigenvalues and eigenvectors of a as well as the components of v in the eigenvector basis the formulas simplify when the matrix a is normal for a non normal we derive upper and lower bounds that are simpler than the exact expressions we also show how to generate starting vectors such that the distance to the krylov subspace is equal to the worst possible case

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

a generalization of saad s bound on harmonic ritz vectors of hermitian matrices abstract we prove a saad s type bound for harmonic ritz vectors of a hermitian matrix the new bound reveals a dependence of the harmonic rayleigh ritz procedure on the condition number of a shifted problem operator several practical implications are discussed in particular the bound motivates incorporation of preconditioning into the harmonic rayleigh ritz scheme

a refined iterative algorithm based on the block arnoldi process for large unsymmetric eigenproblems when the matrix in question is unsymmetric the approximate eigenvectors or ritz vectors obtained by orthogonal projection methods including arnoldi s method and the block arnoldi method cannot be guaranteed to converge in theory even if the corresponding approximate eigenvalues or ritz values do in order to circumvent this danger a new strategy has been proposed by the author for arnoldi s method the strategy used is generalized to the block arnoldi method in this paper it discards ritz vectors and instead computes refined approximate eigenvectors by small sized singular value decompositions it is proved that the new strategy can guarantee the convergence of refined approximate eigenvectors if the corresponding ritz values do the resulting refined iterative algorithm is realized by the block arnoldi process numerical experiments show that the refined algorithm is much more efficient than the iterative block arnoldi algorithm