experimental study of ilu preconditioners for indefinite matrices incomplete lu factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices however their failure rate is still too high for them to be useful as black box library software for general matrices besides fatal breakdowns due to zero pivots the major causes of failure are inaccuracy and instability of the triangular solves when there are small pivots both these problems can occur but these problems can also occur without small pivots through examples from actual problems this paper shows how these problems evince themselves how these problems can be detected and how these problems can sometimes be circumvented through pivoting reordering scaling perturbing diagonal elements and preserving symmetric structure the goal of this paper is to gain a better practical understanding of ilu preconditioners and help improve their reliability

optimality assessment in the enzyme linked immunosorbent assay elisa an optimality criterion is proposed for evaluating the precision of alternative designs in the enzyme linked immunosorbent assay assay profiles are represented as four parameter logistic functions with parameter estimation based on either a weighted nonlinear regression or a simple nonlinear regression after a logarithmic transformation assay design changes are characterized in terms of their effects on parameters in the four parameter logistic model general optimality results are derived for the variance of relative potency estimates in routine assay applications

li yau gradient bounds on compact manifolds under nearly optimal curvature conditions abstract we prove li yau type gradient bounds for the heat equation either on manifolds with fixed metric or under the ricci flow in the former case the curvature condition is r i c l p for some p n 2 or sup m m r i c 2 y d 2 n x y d y where n is the dimension of the manifold in the later case one only needs scalar curvature being bounded we will explain why the conditions are nearly optimal and give an application the li yau bound for the heat equation on manifolds with fixed metric seems to be the first one allowing ricci curvature not bounded from below

gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces abstract let m n g e d v be a smooth metric measure space in this paper we derive a series of gradient estimates and a harnack inequality for positive solutions of a nonlinear parabolic partial differential equation t u q u a u ln u in m n where q c 2 1 m n and a r

li yau type estimates for a nonlinear parabolic equation on complete manifolds abstract let m g be a complete noncompact riemannian manifold with the m dimensional bakry emery ricci curvature bounded below in this paper we give a local li yau type gradient estimate for the positive solutions to a general nonlinear parabolic equation u t u u a u log u q u in m 0 where a r is a c 2 smooth function and q q x t is a function which generalizes many previous well known gradient estimate results

elliptic gradient estimates for a nonlinear heat equation and applications abstract in this paper we study elliptic gradient estimates for a nonlinear f heat equation which is related to the gradient ricci soliton and the weighted log sobolev constant of smooth metric measure spaces precisely we obtain hamilton s and souplet zhang s gradient estimates for positive solutions to the nonlinear f heat equation only assuming the bakry emery ricci tensor is bounded below as applications we prove parabolic liouville properties for some kind of ancient solutions to the nonlinear f heat equation some special cases are also discussed

gradient estimates and harnack inequalities of a parabolic equation under geometric flow abstract in this paper we consider a manifold evolving by a general geometric flow and study parabolic equation q x t t u x t a u x t x t m 0 t we establish space time gradient estimates for positive solutions and elliptic type gradient estimates for bounded positive solutions of this equation by integrating the gradient estimates we derive the corresponding harnack inequalities finally as applications we give gradient estimates of some specific parabolic equations

detecting heteroscedasticity in nonparametric regression summary diagnostic tests and plots are proposed for detecting heteroscedasticity in nonparametric regression the large and small sample power properties are studied for a class of test statistics for the hypothesis of homogeneous variances new diagnostic plots are also developed and illustrated

choosing near linear parameters in the four parameter logistic model for radioligand and related assays ten parameters extracted from six currently used parametrizations of the four parameter logistic model and one new proposal were examined for their statistical behavior in nonlinear least squares estimation in combination with elisa and ria data those which are adequately near linear on the basis of the lowry morton lambda statistic were identified and can be recommended for use in practice

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

comparison geometry for the bakry emery ricci tensor for riemannian manifolds with a measure m g edvolg we prove mean curvature and volume comparison results when the bakry emery ricci tensor is bounded from below and f is bounded or rf is bounded from below generalizing the classical ones i e when f is constant this leads to extensions of many theorems for ricci curvature bounded below to the bakry emery ricci tensor in particular we give extensions of all of the major comparison theorems when f is bounded simple examples show the bound on f is necessary for these results

a matrix li yau hamilton estimate for kahler ricci flow in this paper we prove a new matrix li yau hamilton lyh estimate for kahler ricci flow on manifolds with nonnegative bisectional curvature the form of this new lyh estimate is obtained by the interpolation consideration originated in ch by chow this new inequality is shown to be connected with perelman s entropy formula through a family of differential equalities in the rest of the paper we show several applications of this new estimate and its corresponding estimate for linear heat equation these include a sharp heat kernel comparison theorem generalizing the earlier result of li and tian lt a manifold version of stoll s theorem st on the characterization of algebraic divisors and a localized monotonicity formula for analytic subvarieties which sharpens the bishop volume comparison theorem motivated by the connection between the heat kernel estimate and the reduced volume monotonicity of perelman p we prove a sharp lower bound heat kernel estimate for the time dependent heat equation which is in a certain sense dual to perelman s monotonicity of the reduced volume as an application of this new monotonicity formula we show that the blow down limit of a certain type long time solution is a gradient expanding soliton we also illustrate the connection between the new lyh estimate and the hessian comparison theorem of fin on the forward reduced distance local monotonicity formulae on entropy and forward reduced volume are also derived

gradient estimates for the heat equation under the ricci flow the paper considers a manifold m evolving under the ricci flow and establishes a series of gradient estimates for positive solutions of the heat equation on m

gradient estimates for a simple elliptic equation on complete non compact riemannian manifolds in this paper we study the local gradient estimate for the positive solution to the following equation u aulog u bu 0i nm where a 0 b are real constants m is a complete non compact riemannian manifold our result is optimal in the sense when m g is a complete non compact expanding gradient ricci soliton by definition m g is called an expanding gradient ricci soliton if for some constant c 0 it satisfies that rc cg d 2 f

approximate inverse preconditioners via sparse sparse iterations the standard incomplete lu ilu preconditioners often fail for general sparse indefinite matrices because they give rise to unstable factors l and u in such cases it may be attractive to approximate the inverse of the matrix directly this paper focuses on approximate inverse preconditioners based on minimizing i am f where am is the preconditioned matrix an iterative descent type method is used to approximate each column of the inverse for this approach to be efficient the iteration must be done in sparse mode i e with sparse matrix by sparse vector operations numerical dropping is applied to maintain sparsity compared to previous methods this is a natural way to determine the sparsity pattern of the approximate inverse this paper describes newton global and column oriented algorithms and discusses options for initial guesses self preconditioning and dropping strategies some limited theoretical results on the properties and convergence of approximate inverses are derived numerical tests on problems from the harwell boeing collection and the fidap fluid dynamics analysis package show the strengths and limitations of approximate inverses finally some ideas and experiments with practical variations and applications are presented

ricci deformation of the metric on complete noncompact riemannian manifolds soit m une variete de riemann complete non compacte a n dimensions n 3 pour c1 c2 0 et 0 il existe une constante e e n c1 c2 0 telle que si la courbure de m satisfait a vol b x y c 1 n x m 0 et b rm 2 er 2 0 r c 2 x 0 x 2 x m alors l equation d evolution g ij t t 2r ij t g ij 0 g ij a une solution pour tout temps 0 t et la metrique g ij t converge vers une metrique lisse g ij quand t telle que r ijkl 0 sur m

rational krylov sequence methods for eigenvalue computation abstract algorithms to solve large sparse eigenvalue problems are considered a new class of algorithms which is based on rational functions of the matrix is described the lanczos method the arnoldi method the spectral transformation lanczos method and rayleigh quotient iteration all are special cases but there are also new algorithms which correspond to rational functions with several poles in the simplest case a basis of a rational krylov subspace is found in which the matrix eigenvalue problem is formulated as a linear matrix pencil with a pair of hessenberg matrices

new li yau hamilton inequalities for the ricci flow via the space time approach we prove li yau hamilton inequalties that extend hamilton s matrix inequality for solutions of the ricci flow with nonnegative curvature operators to obtain our extensions we apply the space time formalism of s c chu and one of the authors to solutions of the ricci flow modified by a cosmological constant then we adjoin to the ricci flow the evolution of a 1 form and a 2 form flowing by a system of heat type equations by a rescaling argument the inequalities we obtain in this manner yield new inequalities which are reminiscent of the linear trace inequality of hamilton and one of the authors

a stability analysis of incomplete lu factorizations abstract the combination of iterative methods with preconditionings based on incomplete lu factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations in this paper we show that there are some settings in which the incomplete lu preconditioners are not effective and we demonstrate that their poor performance is due to numerical instability our analysis consists of an analytic and numerical study of a sample two dimensional non self adjoint elliptic problem discretized by several finite difference schemes author

rational approximation preconditioners for sparse linear systems this paper presents a class of preconditioning techniques which exploit rational function approximations to the inverse of the original matrix the matrix is first shifted and then an incomplete lu factorization of the resulting matrix is computed the resulting factors are then used to compute a better preconditioner for the original matrix since the incomplete factorization is made on a shifted matrix a good lu factorization is obtained without allowing much fill in the result needs to be extrapolated to the nonshifted matrix thus the main motivation for this process is to save memory the method is useful for matrices whose incomplete lu factorizations are poor e g unstable

modeling and identifying optimum designs for fitting dose response curves based on raw optical density data abstract for raw optical density rod data such as those generated in biological assays using a 96 well plate reader d optimal designs are identified for a family of homogeneous nonlinear models with two parameters developed for fitting and studying dose response curves further within the class of k point equally spaced and uniform designs d optimal designs are specified also the d efficiency of the d optimal equally spaced and uniform k point designs are compared to d optimal design for 3 k 7 the efficiency robustness of these optimal designs with respect to initial nominal values of the parameters are investigated in addition d optimal designs are derived for a family of heterogeneous nonlinear models