stability and convergence of the difference methods for the space time fractional advection diffusion equation abstract in this paper we consider a space time fractional advection dispersion equation stfade on a finite domain the stfade is obtained from the standard advection dispersion equation by replacing the first order time derivative by the caputo fractional derivative of order 0 1 and the first order and second order space derivatives by the riemman liouville fractional derivatives of order 0 1 and of order 1 2 respectively for the space fractional derivatives d x u x t and d x u x t we adopted the grunwald formula and the shift grunwald formula respectively we propose an implicit difference method idm and an explicit difference method edm to solve this equation stability and convergence of these methods are discussed using mathematical induction we prove that the idm is unconditionally stable and convergent but the edm is conditionally stable and convergent numerical results are in good agreement with theoretical analysis

on maximum entropy and minimum kl divergence optimization by grobner basis methods in this paper we study constrained maximum entropy and minimum divergence optimization problems in the cases where integer valued sufficient statistics exists using tools from computational commutative algebra we show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations we give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a grobner basis method to compute it in the cases of minimum kl divergence models we show that implicitization preserves specialization of prior distribution this result leads us to a grobner basis method to embed minimum kl divergence models in algebraic varieties c 2012 elsevier inc all rights reserved

on new exponential quadratically convergent iterative formulae a class of exponential iterative formulae having quadratic convergence is discussed in this paper the theoretical analysis and numerical experiments show that new exponential iterative formulae are effective and comparable to well known method of newton

iterative image reconstruction algorithms based on cross entropy minimization the related problems of minimizing the functionals f x alpha kl y px 1 alpha kl p x and g x alpha kl px y 1 alpha kl x p respectively over the set of vectors x or 0 are considered kl a b is the cross entropy or kullback leibler distance between two nonnegative vectors a and b iterative algorithms for minimizing both functionals using the method of alternating projections are derived a simultaneous version of the multiplicative algebraic reconstruction technique mart algorithm called smart is introduced and its convergence is proved

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

a note on the geometric interpretation of the em algorithm in estimating item characteristics and student abilities this note uses the em algorithm in an item response model as an illustration of a general method of parameter estimation which geometrically can be described as an alternating projection method

block iterative methods for image reconstruction from projections the simultaneous mart algorithm smart and the expectation maximization method for likelihood maximization emml are extended to block iterative versions bi smart and bi emml that converge to a solution in the feasible case for any choice of subsets the bi emml reduces to the ordered subset emml of hudson et al 1992 1994 when their subset balanced property holds

generalized scalings satisfying linear equations abstract we unify and generalize a broad class of problems referred in the literature as scaling problems by extending the applicability of a formulation suggested recently by bapat and raghavan specifically let a r n b r m and c r m n be given where a is strictly positive a c scaling of the vector a is defined to be a vector a r n with a i a i m k 1 u c kj k for some strictly positive vector u r m the problem of finding a c scaling of the vector a which satisfies the linear system cx b will be called a generalized scaling problem in this paper it is shown that previously studied matrix scaling problems e g finding scalings with prespecified row sums and column sums or finding scalings with row sums equaling the corresponding column sums or finding scalings of multidimensional matrices with prespecified margins are special instances of generalized scaling problems generalized scaling problems are reduced to convex optimization problems and the reduction is used to characterize solutions to develop necessary and sufficient conditions for their existence to establish uniqueness results and to characterize approximate solutions

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

an iterative procedure for obtaining i projections onto the intersection of convex sets abstract a frequently occuring problem is to find that probability distribution pd lying within a convex set which minimizes the i divergence between it and given pd r this document proposes an iterative procedure which requires only that the set be convex and not necessarily linear which under general conditions will converge to the desired i projection

regularization on graphs with function adapted diffusion processes harmonic analysis and diffusion on discrete data has been shown to lead to state of the art algorithms for machine learning tasks especially in the context of semi supervised and transductive learning the success of these algorithms rests on the assumption that the function s to be studied learned interpolated etc are smooth with respect to the geometry of the data in this paper we present a method for modifying the given geometry so the function s to be studied are smoother with respect to the modified geometry and thus more amenable to treatment using harmonic analysis methods among the many possible applications we consider the problems of image denoising and transductive classification in both settings our approach improves on standard diffusion based methods

the analytical solution and numerical solution of the fractional diffusion wave equation with damping fractional partial differential equations have been applied to many problems in physics finance and engineering numerical methods and error estimates of these equations are currently a very active area of research in this paper we consider a fractional diffusionwave equation with damping we derive the analytical solution for the equation using the method of separation of variables an implicit difference approximation is constructed stability and convergence are proved by the energy method finally two numerical examples are presented to show the effectiveness of this approximation

positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums abstract in this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums these conditions are variations of bapat raghavan and franklin lorenz conditions

a moment based variational approach to tomographic reconstruction we describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood ml estimates of its orthogonal moments we show how these estimated moments and their correlated error statistics can be computed directly and in a linear fashion from given noisy and possibly sparse projection data moreover thanks to the consistency properties of the radon transform this two step approach moment estimation followed by image reconstruction can be viewed as a statistically optimal procedure furthermore by focusing on the important role played by the moments of projection data we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments taking advantage of this connection our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data we show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem we show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back projection fbp algorithm

a new superconvergence property of wilson nonconforming finite element in this paper the wilson nonconforming finite element method is considered to solve a class of two dimensional second order elliptic boundary value problems a new superconvergence property at the vertices and the midpoints of four edges of rectangular meshes is obtained

analytical solution of a fractional diffusion equation by adomian decomposition method this paper presents an analytical solution of a fractional diffusion equation by adomian decomposition method by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

methods for scaling to doubly stochastic form abstract new methods for scaling square nonnegative matrices to doubly stochastic form are described a generalized version of the convergence theorem of sinkhorn and knopp 1967 is proved and applied to show convergence for these new methods tests indicate that one of the new methods has significantly better average and worst case behavior than the sinkhorn knopp method for one of the 3 3 examples of marshall and olkin 1968 sk requires 130 times as many operations as the new algorithm to achieve row and column sums 1 10 5

a mixed finite element method for a time fractional fourth order partial differential equation in this paper a numerical theory based on the mixed finite element method for a time fractional fourth order partial differential equation pde is presented and analyzed an auxiliary variable email protected is introduced then the fourth order equation can be split into the coupled system of two second order equations the time caputo fractional derivative is discretized by a finite difference method and the spatial direction is approximated by the mixed finite element method the stabilities based on a priori analysis for two variables are discussed and some a priori error estimates in l 2 norm for the scalar unknown u and the variable email protected are derived respectively moreover an a priori error result in h 1 norm for the scalar unknown u also is proved for verifying the theoretical analysis a numerical test is made by using matlab procedure

high order finite element methods for time fractional partial differential equations the aim of this paper is to develop high order methods for solving time fractional partial differential equations the proposed high order method is based on high order finite element method for space and finite difference method for time optimal convergence rate o dt 2 a n r is proved for the r 1 th order finite element method r 2

a new approach of superconvergence analysis for two dimensional time fractional diffusion equation abstract in this paper a new approach of superconvergent estimate of bilinear finite element is established for two dimensional time fractional diffusion equation under fully discrete scheme the novelty of this approach is the combination technique of the interpolation and ritz projection as well as the superclose estimate in h 1 norm between them which avoids the difficulty of constructing a postprocessing operator for ritz projection operator and reduces the regularity requirement of the exact solution at the same time three numerical examples are carried out to verify the theoretical analysis

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

information theoretic image formation the emergent role of information theory in image formation is surveyed unlike the subject of information theoretic communication theory information theoretic imaging is far from a mature subject the possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem for defining measures of optimality used to form estimates of images for addressing issues associated with the development of algorithms based on these optimality criteria and for quantifying the quality of the approximations the definition of the imaging problem consists of an appropriate model for the data and an appropriate model for the reproduction space which is the space within which image estimates take values each problem statement has an associated optimality criterion that measures the overall quality of an estimate the optimality criteria include maximizing the likelihood function and minimizing mean squared error for stochastic problems and minimizing squared error and discrimination for deterministic problems the development of algorithms is closely tied to the definition of the imaging problem and the associated optimality criterion algorithms with a strong information theoretic motivation are obtained by the method of expectation maximization related alternating minimization algorithms are discussed in quantifying the quality of approximations global and local measures are discussed global measures include the mean squared error and discrimination between an estimate and the truth and probability of error for recognition or hypothesis testing problems local measures include fisher information

scalings of matrices which have prespecified row sums and column sums via optimization abstract the problem of scaling a matrix so that it has given row and column sums is transformed into a convex minimization problem in particular we use this transformation to characterize the existence of such scaling or corresponding approximations we obtain new results as well as new streamlined proofs of known results

an analysis of the properties of the variants of newton s method with third order convergence for the last five years the variants of the newton s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non linear equations these methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives in this paper we investigate about the relationship between these methods which are in fact based on the approximation of the second order derivative present in the third order limited taylor expansion we also prove that they are different forms of the halley method and are all contractive iterative methods in a common neighbourhood we extend some of these variants to multivariate cases and prove their respective local cubic convergence from their corresponding linear models

a class of onto multifunctions a convex valued upper continuous multifunction with pointed closed convex domain is proved to be onto if there is a selection with certain coercive properties and if the selection for each point lies in the affine hull of the smallest face of the domain containing the point the proof uses a piecewise affine homotopy construction we apply the onto theorem to an approximation of a network of servers and show that arbitrary congestion levels can be realized with appropriate arrival levels

order independence and factor convergence in iterative scaling abstract we prove two results concerning iterative scaling which have been claimed but not proved by other authors in the field iterative scaling is a procedure which begins with a probability measure q on a finite set x and a finite set of partition constraints on x it produces a sequence of iterates p0 q p1 pt in which each pt t 62 0 is an adjustment scaling of pt 1 to fit a single set of prescribed partition constraints under fairly general hypotheses the iterates pt converge to the unique probability p which simultaneously satisfies the given constraints and is exponentially equivalent to the starting measure q or equivalently which minimizes the i divergence d p q over all probabilities p on x which satisfy the constraints the first main result theorem 3 1 states that the convergence of iterative scaling to the unique limit is independent of the order in which the adjustments for the prescribed partition constraints are made provided each adjustment is made infinitely many times the second main result theorem 4 2 is that under certain commonly satisfied conditions each factor of the exponential form being built up within the algorithm one factor for each partition constraint converges separately a third group of results sections 5 6 provides an account of the relationship between the probability measures which satisfy all of the constraints and those which are exponentially equivalent to q

matrix scaling entropy minimization and conjugate duality i existence conditions abstract we have four primary objectives in this paper first we introduce a problem called truncated matrix scaling that generalizes two well studied matrix scaling problems diagonal similarity scaling and fixed row column equivalence scaling second we derive necessary and sufficient conditions for the attainment of the infimum in the fenchel dual of a class of convex optimization problems third we show that existence of a solution for truncated matrix scaling is equivalent to the attainment of the infimum in a corresponding dual optimization problem we thereby derive necessary and sufficient conditions for the existence of a solution for truncated matrix scaling fourth we derive known existence conditions for similarity and equivalence scaling from the conditions for truncated matrix scaling

applications of an inequality in information theory to matrices abstract if x and y are nonnegative vectors of order n and if n i 1 x i n i 1 y i then a well known inequality asserts that n i 1 x x i i n i 1 y x i i with equality if and only if x y in this paper various situations are considered where this inequality can be applied to obtain inequalities concerning nonnegative matrices in particular inequalities are proved concerning nonnegative matrices which are diagonally equivalent permanents and functions more general than the permanent and diagonal products and circuit products of nonnegative matrices

on dykstra s iterative fitting procedure this paperp shows that dykstra s procedure for finding the i projection onto the intersection of closed convex sets holds in general it does this by first showing that each of the i projections onto individual convex sets defined in dykstra s iterative procedure exists and that no condition such as imposed by dykstra is required to prove the convergence of the iterative procedure to a unique i projection

an iterative procedure for general probability measures to obtain i projections onto intersections of convex sets the iterative proportional fitting procedure ipfp was introduced formally by deming and stephan in 1940 for bivariate densities this procedure has been investigated by kullback and ruschendorf it is well known that the ipfp is a sequence of successive i projections onto sets of probability measures with fixed marginals however when finding the i projection onto the intersection of arbitrary closed convex sets e g marginal stochastic orders a sequence of successive i projections onto these sets may not lead to the actual solution addressing this situation we present a new iterative i projection algorithm under reasonable assumptions and using tools from fenchel duality convergence of this algorithm to the true solution is shown the cases of infinite dimensional ipfp and marginal stochastic orders are worked out in this context

maximum likelihood estimation in log linear models we study maximum likelihood estimation in log linear models under conditional poisson sampling schemes we derive necessary and sufficient conditions for existence of the maximum likelihood estimator mle of the model parameters and investigate estimability of the natural and mean value parameters under a nonexistent mle our conditions focus on the role of sampling zeros in the observed table we situate our results within the framework of extended exponential families and we exploit the geometric properties of log linear models we propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log linear model analysis

choosing parameters in block iterative or ordered subset reconstruction algorithms viewed abstractly all the algorithms considered here are designed to provide a nonnegative solution x to the system of linear equations y px where y is a vector with positive entries and p a matrix whose entries are nonnegative and with no purely zero columns the expectation maximization maximum likelihood method as it occurs in emission tomography and the simultaneous multiplicative algebraic reconstruction technique are slow to converge on large data sets accelerating convergence through the use of block iterative or ordered subset versions of these algorithms is a topic of considerable interest these block iterative versions involve relaxation and normalization parameters the correct selection of which may not be obvious to all users the algorithms are not faster merely by virtue of being block iterative the correct choice of the parameters is crucial through a detailed discussion of the theoretical foundations of these methods we come to a better understanding of the precise roles these parameters play

new iterative methods abstract in this paper we present a new three step predictor corrector type iterative method for finding simple and real roots of a non linear equation in one variable i e f x 0 experiments show that our new method is more efficient than the other known methods a comparison of the proposed method with other methods reveals that the new method performs better as shown in table 2

fourth order convergent iterative method for nonlinear equation in this paper we suggest and analyze a new iterative method for finding approximate solution of the nonlinear equation f x 0 it is shown that proposed method has fourth order convergence several numerical examples are given to illustrate that the method developed in this paper give better results than the other methods including newton method

d1ad2 theorems for multidimensional matrices abstract a new technique for proving d 1 ad 2 theorems is given also a generalization of d 1 ad 2 theorems to multidimensional matrices is indicated

an extension of a theorem of darroch and ratcliff in loglinear models and its application to scaling multidimensional matrices abstract let c c ij be an m n matrix with real entries let b be any nonzero m vector let k c b 0 be bounded let x x 1 x 2 x n y y 1 y 2 y n be two nonnegative vectors with y k and x j 0 y j 0 for any coordinate j then it is shown that there exists a k and positive numbers z 1 z 2 z m such that j x j m i 1 z c ij i for all j th theorem slightly generalizes a theorem of darroch and ratcliff in loglinear models with a completely different proof technique the proof relies on an extension of a topological theorem of kronecker to set valued maps and the duality theorem of linear programming many theorems in scaling of matrices and multidimensional matrices are direct consequences of this theorem the main idea is to associate a suitable zero one matrix of transportation with any multidimensional matrix some motivations for scaling applications are also discussed

finite difference finite element method for a nonlinear time fractional fourth order reaction diffusion problem abstract in this article a finite difference finite element algorithm which is based on a finite difference approximation in time direction and finite element method in spatial direction is presented and discussed to cast about for the numerical solutions of a time fractional fourth order reaction diffusion problem with a nonlinear reaction term to avoid the use of higher order elements the original problem with spatial fourth order derivative need to be changed into a second order coupled system by introducing an intermediate variable u then the fully discrete finite element scheme is formulated by using a finite difference approximation for time fractional and integer derivatives and finite element method in spatial direction the unconditionally stable result in the norm which just depends on initial value and source item is derived some a priori estimates of l 2 norm with optimal order of convergence o t 2 h m 1 where t and h are time step length and space mesh parameter respectively are obtained to confirm the theoretical analysis some numerical results are provided by our method

the use of finite difference element approaches for solving the time fractional subdiffusion equation in this paper two finite difference element approaches for the time fractional subdiffusion equation with dirichlet boundary conditions are developed in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method the two methods are unconditionally stable and convergent of order o tau q h r 1 in the l 2 norm where q 2 beta or 2 when the analytical solution to the subdiffusion equation is sufficiently smooth beta 0 beta 1 is the order of the fractional derivative tau and h are the step sizes in time and space respectively and r is the degree of the polynomial space the corresponding schemes for the subdiffusion equation with neumann boundary conditions are presented as well where the stability and convergence are shown numerical examples are provided to verify the theoretical analysis comparisons between the algorithms derived in this paper and the existing algorithms are given

analytical solution of a fractional diffusion equation by variational iteration method in the present paper the analytical approximate solution of a fractional diffusion equation is deduced with the help of powerful variational iteration method by using an initial value the explicit solutions of the equation for different cases have been derived which accelerate the rapid convergence of the series solution the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of the problem are presented graphically

on the scaling of multidimensional matrices abstract elementary proofs are given for theorems of bapat and raghavan on the scaling of nonnegative multidimensional matrices theorems of sinkhorn and of brualdi parter and schneider are derived as corollaries for positive two dimensional matrices hilbert s projective metric and a theorem of g birkhoff are used to prove that sinkhorn s original iterative procedure converges geometrically the ratio of convergence is estimated from the given data

matrix scaling a geometric proof of sinkhorn s theorem abstract matrix scaling problems have been extensively studied since sinkhorn established in 1964 the following result any positive square matrix of order n is diagonally equivalent to a unique doubly stochastic matrix of order n and the diagonal matrices which take part in the equivalence are unique up to scalar factors we present a new elementary proof of the existence part of sinkhorn s theorem which is based on well known geometrical interpretations of doubly stochastic matrices and left and right multiplication by diagonal matrices

free steering relaxation methods for problems with strictly convex costs and linear constraints we consider dual coordinate ascent methods for minimizing a strictly convex possibly nondifferentiable function subject to linear constraints such methods are useful in large scale applications e g entropy maximization quadratic programming network flow because they are simply can exploit sparsity and in certain cases are highly parallelizable we establish their global convergence under weak conditions and a free steering order of relaxation previous comparable results were restricted to special problems with separable costs and equality constraints our convergence framework unifies to a certain extent the approaches of bregman censor and lent de pierro and iusem and luo and tseng and complements that of bertsekas and tseng

on pairs of multidimensional matrices abstract recently bapat applied a topological theorem of kronecker and generalized a theorem of sinkhorn on positive matrices here we give an alternative proof of a slightly stronger version of his generalization this proof combines kakutani s fixed point theorem and the duality theorem of linear programming and gives yet another proof of a theorem of bacharach and menon on pairs of nonnegative matrices

a new iterative method for solving nonlinear equations abstract in this paper we present a new efficient iterative method for solving nonlinear equations improving newton raphson method this method is based on a modification of the proposal of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 the convergence properties of the method and some other methods are discussed some numerical illustrations are given to show that the proposed method behaves equal or better performance compared to the other methods of same kind

fractional diffusion in inhomogeneous media starting from the continuous time random walk ctrw scheme with the space dependent waiting time probability density function pdf we obtain the time fractional diffusion equation with varying in space fractional order of time derivative as an example we study the evolution of a composite system consisting of two separate regions with different subdiffusion exponents and demonstrate the effects of non trivial drift and subdiffusion whose laws are changed in the course of time

p1 nonconforming quadrilateral finite element methods for second order elliptic problems a p1 nonconforming quadrilateral finite element is introduced for second order elliptic problems in two dimensions unlike the usual quadrilateral nonconforming finite elements which contain quadratic polynomials or polynomials of degree greater than 2 our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges one of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom among the nonconforming quadrilateral elements an optimal rate of convergence is obtained also a nonparametric reference scheme is introduced in order to systematically compute stiffness and mass matrices on each quadrilateral an extension of the p1 nonconforming element to three dimensions is also given finally several numerical results are reported to confirm the effective nature of the proposed new element

the rate of convergence of sinkhorn balancing abstract we prove that sinkhorn balancing always converges linearly provided the starting matrix has total support for our purposes we define sinkhorn balancing as the iteration x t 1 f x t where f is thattransformation on row stochastic matrices x defined by first balancing the columns of x and then the rows the proof hinges on determining the precise nature of the eigenspace of the maximal eigenvalue 1 of the jacobian matrix j f of f evaluated at the limiting doubly stochastic matrix d lim t x t we examine the spectral properties of the jacobian matrix for a class of growth transformations which contains f then we prove a generalization of ostrowski s theorem on linear convergence yielding sufficient conditions under which linear convergence occurs in the presence of eigenvalues of j f of modulus 1

approximating the permanent via importance sampling with application to the dimer covering problem we estimate the asymptotic growth rate of the number of dimer covers of a cubic lattice our estimate 3 0 4466 0 0006 is consistent with the lower bounds obtained by hammersley and later schrijver and the more recent improved upper bound obtained by ciucu obtaining this estimate is an important step toward approximating the partition function of the cubic monomer dimer system from the partition function all of the standard thermodynamic quantities can be evaluated it is well known that computing 3 is equivalent to computing the permanent of a certain 0 1 matrix we describe an extremely efficient monte carlo algorithm for approximating the permanent previous work on monte carlo approaches includes the pioneering results of jerrum and sinclair who use a rapidly mixing random walk our method is inspired by results of soules on convergence of sinkhorn balancing to obtain a maximum entropy doubly stochastic matrix we use the sinkhorn balanced matrix to generate an importance function that allows us to do direct random sampling rather than a random walk that converges to a limiting distribution

ilu preconditioners for nonsymmetric saddle point matrices with application to the incompressible navier stokes equations motivated by the numerical solution of the linearized incompressible navier stokes equations we study threshold incomplete lu factorizations for nonsymmetric saddle point matrices the resulting preconditioners are used to accelerate the convergence of a krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions the paper presents and examines an extension for nonsymmetric matrices of the tismenetsky kaporin incomplete factorization it is shown that in numerically challenging cases of higher reynolds number flows one benefits from using this two parameter modification of a standard threshold ilu preconditioner the performance of the ilu preconditioners is studied numerically for a wide range of flow and discretization parameters and the efficiency of the approach is shown if threshold parameters are chosen suitably the practical utility of the method is further demonstrated for the haemodynamic problem of simulating blood flow in a right c