convergent finite difference solvers for viscosity solutions of the elliptic monge ampere equation in dimensions two and higher the elliptic monge ampere equation is a fully nonlinear partial differential equation that originated in geometric surface theory and has been applied in dynamic meteorology elasticity geometric optics image processing and image registration solutions can be singular in which case standard numerical approaches fail novel solution methods are required for stability and convergence to the weak viscosity solution in this article we build a wide stencil finite difference discretization for the monge ampere equation the scheme is monotone so the barles souganidis theory allows us to prove that the solution of the scheme converges to the unique viscosity solution of the equation solutions of the scheme are found using a damped newton s method we prove convergence of newton s method and provide a systematic method to determine a starting point for the newton iteration computational results are presented in two and three dimensions which demonstrates the speed and accuracy of the method on a number of exact solutions which range in regularity from smooth to nondifferentiable

stability criteria of linear neutral systems with multiple delays in the present note stability of linear neutral systems with multiple delays is investigated by principle of the argument stability criteria are derived which are necessary and sufficient for asymptotic stability of the neutral systems the stability criteria need only to evaluate the characteristic function and the argument on the boundary of a certain rectangular region several numerical examples are given to illustrate the results

a continuous linear optimal transport approach for pattern analysis in image datasets we present a new approach to facilitate the application of the optimal transport metric to pattern recognition on image databases the method is based on a linearized version of the optimal transport metric which provides a linear embedding for the images hence it enables shape and appearance modeling using linear geometric analysis techniques in the embedded space in contrast to previous work we use monge s formulation of the optimal transport problem which allows for reasonably fast computation of the linearized optimal transport embedding for large images we demonstrate the application of the method to recover and visualize meaningful variations in a supervised learning setting on several image datasets including chromatin distribution in the nuclei of cells galaxy morphologies facial expressions and bird species identification we show that the new approach allows for high resolution construction of modes of variations and discrimination and can enhance classification accuracy in a variety of image discrimination problems highlightsa continuous version of the lot framework is described that bypasses many of the difficulties associated with the discrete formulation using continuous transport maps a forward and inverse transform operation is defined for images an improved reference average image estimation algorithm is proposed the range within which points in lot space are invertible according to the continuous formulation is calculated we show that our method significantly speeds up the computation of the lot embedding

inertia controlling methods for general quadratic programming active set quadratic programming qp methods use a working set to define the search direction and multiplier estimates in the method proposed by fletcher in 1971 and in several subsequent mathematically equivalent methods the working set is chosen to control the inertia of the reduced hessian which is never permitted to have more than one nonpositive eigenvalue such methods will be called inertia controlling this paper presents an overview of a generic inertia controlling qp method including the equations satisfied by the search direction when the reduced hessian is positive definite singular and indefinite recurrence relations are derived that define the search direction and lagrange multiplier vector through equations related to the karush kuhn tucker system discussion is included of connections with inertia controlling methods that maintain an explicit factorization of the reduced hessian matrix

simultaneous finite and infinite zero assignments of linear systems abstract a simultaneous finite and infinite zero assignment problem via sensor selection for linear multivariable systems is proposed by sensor selection we mean an appropriate choice of the output matrix c here by utilizing the well known burnovsky canonical form for a linear system characterized by the matrix pair a b we obtain an explicit construction algorithm that generates a non empty set c of output matrices such that for any member c of this set the corresponding system characterized by the triple a b c has the prescribed finite and infinite zero structures two examples are also given to illustrate our results

deflated decomposition of solutions of nearly singular systems when solving the linear system ax b where a may be nearly singular and b is not consistent with a one is often interested in computing a deflated solution i e a unique solution to a nearby singular but consistent system a s x d tilde b kelley 14 15 has considered deflated solutions with a s corresponding to setting a small pivot of the lu factorization of a to zero stewart 22 proposed an iterative algorithm for computing a deflated solution with a s corresponding to setting the smallest singular value of a to zero kelley s approach explicitly uses submatrices of the lu factors whereas stewart s approach is implicit in that it only involves solving systems with a in this paper we generalize the concept of a deflated solution to that of a deflated decomposition which expresses the solution x in terms of x d and the null vectors of a s we treat such decompositions in a uniform framework that includes the approaches of kelley and stewart and introduce some new deflated

optimal mass transport for higher dimensional adaptive grid generation in this work we describe an approach for higher dimensional adaptive grid generation based on solving the l 2 monge kantorovich problem mkp which is a special case of the classical optimal mass transportation problem two methods are developed for computing the coordinate transformation used to define the grid adaptation for the first method the transformation is determined by solving a parabolic monge ampere equation for a steady state solution for the second method the grid movement is determined from the velocity field obtained by solving a fluid dynamics formulation of the l 2 mkp several numerical experiments are presented to demonstrate the performance of the mkp methods and to compare them with some related adaptive grid methods the experimental results demonstrate that the mkp methods show promise as effective and reliable methods for higher dimensional adaptive grid generation

a note on the group inverse of some 2 2 block matrices over skew fields abstract let k be a skew field and km n be the set of all m n matrices over k in this paper we give the necessary and sufficient conditions to the existence and the representations of the group inverse for block matrix ax yb a b 0 under some conditions where a y km n x b kn m

an elementary proof of the polar factorization of vector valued functions we present an elementary proof of an important result of y brenier br1 br2 namely that vector fields in d satisfying a nondegeneracy condition admit the polar factorization u x s x where is a convex function and s is a measure preserving mapping brenier solves a minimization problem using monge kantorovich theory whereas we turn our attention to a dual problem whose euler lagrange equation turns out to be

the numerical solution of equality constrained quadratic programming problems this paper proves that a large class of iterative schemes can be used to solve a certain constrained minimization problem the constrained minimization problem considered involves the minimization of a quadratic functional subject to linear equality constraints among this class of convergent iterative schemes are generalizations of the relaxed jacobi gauss seidel and symmetric gauss seidel schemes

on practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem we present practical conditions under which the existence and uniqueness of a finite solution to a given equality quadratic program may be examined different sets of conditions allow this examination to take place when null space range space or lagrangian methods are used to find stationary points for the quadratic program

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

parallel solvers for virtual element discretizations of elliptic equations in mixed form abstract the aim of this paper is twofold on the one hand we numerically test the performance of mixed virtual elements in three dimensions to solve the mixed formulation of three dimensional elliptic equations on polyhedral meshes on the other hand we focus on the parallel solution of the linear system arising from such discretization considering both direct and iterative parallel solvers in the latter case we develop two block preconditioners one based on the approximate schur complement and one on a regularization technique both these topics are numerically validated by several parallel tests performed on a linux cluster more specifically we show that the proposed virtual element discretization recovers the expected theoretical convergence rates and we analyze the performance of the direct and iterative parallel solvers taken into account

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

optimal mass transport for registration and warping image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times in this paper we present a method for computing elastic registration and warping maps based on the monge kantorovich theory of optimal mass transport this mass transport method has a number of important characteristics first it is parameter free moreover it utilizes all of the grayscale data in both images places the two images on equal footing and is symmetrical the optimal mapping from image a to image b being the inverse of the optimal mapping from b to a the method does not require that landmarks be specified and the minimizer of the distance functional involved is uniques there are no other local minimizers finally optimal transport naturally takes into account changes in density that result from changes in area or volume although the optimal transport method is certainly not appropriate for all registration and warping problems this mass preservation property makes the monge kantorovich approach quite useful for an interesting class of warping problems as we show in this paper our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the l2 kantorovich wasserstein or earth mover s distance under a mass preservation constraint we show how this approach leads to practical algorithms and demonstrate our method with a number of examples including those from the medical field we also extend this method to take into account changes in intensity and show that it is well suited for applications such as image morphing

assignment of complete structural properties of linear systems via sensor selection for x ax bu the problem of structural assignment via sensor selection is to find an output equation y cx du such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures as well as the invertibility properties in this paper we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned and an explicit algorithm for constructing the required matrix pair c d

linear algebra methods in a mixed approximation of magnetostatic problems in the solution of magnetostatic problems the use of a mixed formulation based on both the magnetic and magnetic displacement fields is particularly appropriate as it allows us to impose the physical conditions exactly and to maintain the continuity properties of the two fields together with an efficient treatment of boundary conditions the discretization by means of a proper finite element method yields a strongly structured algebraic linear system this paper is concerned with the solution of this large very sparse indefinite linear system in particular we present the implementation of some known direct and preconditioned iterative methods and discuss their performance on two dimensional 2 d and three dimensional 3 d specific models we show that the 2 d system can be efficiently handled by appropriate variants of these schemes while preliminary tests on the 3 d system give some insight in the understanding of the analysis that needs to be done

an efficient numerical method for the solution of the l_2 optimal mass transfer problem in this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal l 2 mass transport mapping in contrast to the integration of a time dependent partial differential equation proposed in s angenent s haker and a tannenbaum siam j math anal 35 2003 pp 61 97 we employ in the present work a direct variational method the efficacy of the approach is demonstrated on both real and synthetic data

a semi free weighting matrices approach for neutral type delayed neural networks in this paper a new approach is proposed for stability issues of neutral type neural networks dnns with constant delay first the semi free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the leibniz newton formula to simplify the system synthesis and to obtain less computation demand second global exponential stability conditions which are less conservative and restrictive than the known results are derived at the same time based on the above approach fewer variable matrices are introduced in the construction of the lyapunov functional and augmented lyapunov functional two examples are given to show their effectiveness and advantages over others

an iteration for indefinite systems and its application to the navier stokes equations for large sparse systems of linear equations iterative solution techniques are attractive in this paper we propose and examine the convergence of an iterative method for an important class of nonsymmetric and indefinite coefficient matrices based on the use of an indefinite and symmetric preconditioner we apply our technique to the linearized navier stokes equations the oseen equations

representations of the drazin inverse for a class of block matrices abstract in this paper we give a formula for the drazin inverse of a block matrix f i i e 0 where e is square and i is the identity matrix further we get representations of the drazin inverse for matrices of the form m a b c 0 where a is square under some conditions expressed in terms of the individual blocks

new stability analysis for linear neutral system via state matrix decomposition this paper deals with the problem of delay dependent stability for neutral systems the matrix decomposition technique is employed to reduce the conservativeness of stability conditions the main results are extended to the neutral system with time varying uncertainties the proposed methods are with simpler form in terms of lmi and better performance than the existing ones in the literatures numerical examples are given to illustrate the effectiveness of the proposed methods

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

matrix pencil characterization of almost a z invariant subspaces a classification of geometric concepts the equivalence between the algebraic matrix pencil characterization of the sub spaces of the extended geometric theory and their dynamic characterization 13 established as a result a complete classification of almost a b invariant a b invariant almost controllability and controllability subspaces is derived in terms of matrix pencil invariants the frequency propagation aspects of infinite spectrum a b invariant subspaces are investigated and it is shown that they are limits of closed loop eigenspaces with arbitrarily largo eigenvalues finally the importance of the infinite frequency subspaces in the study of the asymptotic behaviour of the closed loop eigenspaces and eigenvalues under scalar gain output feedback is discussed

an optimal preconditioner for a class of saddle point problems with a penalty term iterative methods are considered for a class of saddle point problems with a penalty term arising from finite element discretizations of certain elliptic problems an optimal preconditioner which is independent of the discretization and the penalty parameter is constructed this approach is then used to design an iterative method with a convergence rate bounded independently of the lame parameters occurring in the equations of linear elasticity

brief on the problem of general structural assignments of linear systems through sensor actuator selection a systematic method is developed for determining an output matrix c for a given matrix pair a b such that the resulting linear system characterized by the matrix triple a b c has the pre specified system structural properties such as the finite and infinite zero structure and the invertibility structures since the matrix c describes the locations of the sensors the procedure of choosing c is often referred to as sensor selection the method developed in this paper for sensor selection can be applied to the dual problem of actuator selection where for a given matrix pair a c a matrix b is to be determined such that the resulting matrix triple a b c has the pre specified structural properties

preconditioning for the steady state navier stokes equations with low viscosity we introduce a preconditioner for the linearized navier stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero for constant coefficient problems with periodic boundary conditions we show that the preconditioning yields a system with a single eigenvalue equal to 1 so that performance is independent of both viscosity and mesh size for other boundary conditions we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon we also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration with virtually no degradation of performance

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

a class of iterative methods for solving saddle point problems we consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points we are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations we present an iterative method involving two levels of iteration similar in some respects to the uzawa algorithm we relate the rates of convergence of the outer and inner iterations proving that under natural hypotheses the outer iteration achieves the rate of convergence of the inner iteration the technique is applied to finite element approximations of the stokes equations

on the finite transmission zero assignment problem abstract in this paper the problem of finite transmission zero assignment is examined by squaring a system from the outputs to the inputs in particular we study this problem for two cases namely for state accessible and partially state accessible systems we show that the problem of finite transmission zero assignment problem for state accessible systems is equivalent to a pole placement problem with state feedback on a reduced order subspace which always has a solution in the case of partially state accessible systems we show that the finite transmission zero assignment problem is equivalent to a pole placement problem with output feedback on a reduced order subspace which generically has a solution for the case when p m n for both cases we exploit the block hessenberg form of the system and the concept of sylvester equations in order to solve this problem in a computationally efficient manner

fast finite volume simulation of 3d electromagnetic problems with highly discontinuous coefficients we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies and the permeability permittivity and conductivity may vary significantly the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain the present article extends methods we proposed earlier for constant permeability e haber u ascher d aruliah and d oldenburg j comput phys 163 2000 pp 150 171 d aruliah u ascher e haber and d oldenburg math models methods appl sci to appear to handle also problems in which the permeability is variable and may contain significant jump discontinuities in order to address the problem of slow convergence we reformulate maxwell s equations in terms of potentials applying a helmholtz decomposition to either the electric field or the magnetic field the null space of the curl operators can then be annihilated by adding a stabilizing term using a gauge condition and thus obtaining a strongly elliptic differential operator a staggered grid finite volume discretization is subsequently applied to the reformulated pde system this scheme works well for sources of various types even in the presence of strong material discontinuities in both conductivity and permeability the resulting discrete system is amenable to fast convergence of ilu preconditioned krylov methods we test our method using several numerical examples and demonstrate its robust efficiency we also compare it to the classical yee method using similar iterative techniques for the resulting algebraic system and we show that our method is significantly faster especially for electric sources

a framework for equilibrium equations the equations of equilibrium in a wide class of applications share a common structure the discrete case leads to a positive definite symmetric matrix a t ca in which a is rectangular and c is often diagonal the continuous case linear or nonlinear repeats that pattern there is a minimum principle for the potentials and a dual principle for the flow variables we try to clarify these different expressions of the same law

delays dependent region partitioning approach for stability criterion of linear systems with multiple time varying delays abstract this paper considers a delay dependent stability criterion for linear systems with multiple time varying delays to exploit all possible information for the relationships among the marginally delayed states x t i m x t i 1 m the exactly delayed states x t i t x t i 1 t and the current state x t for each pair i i 1 of time varying delays a delays dependent region partitioning approach in double integral terms is proposed by applying the wirtinger based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning a stability criterion is derived in terms of linear matrix inequalities numerical examples show that the resulting criterion outperforms the existing one in literature

on solving block structured indefinite linear systems we consider 2 2 block indefinite linear systems whose 2 2 block is zero such systems arise in many applications we discuss two techniques that are based on modifying the 1 1 block in a way that makes the system easier to solve the main part of the paper focuses on an augmented lagrangian approach a technique that modifies the 1 1 block without changing the system size the choice of the parameter involved the spectrum of the linear system and its condition number are discussed and some analytical observations are provided a technique of deflating the 1 1 block is then introduced finally numerical experiments that validate the analysis are presented

fast nonsymmetric iterations and preconditioning for navier stokes equations discretization and linearization of the steady state navier stokes equations gives rise to a nonsymmetric indefinite linear system of equations in this paper we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization we confirm and supplement these analytic results with a series of numerical experiments indicating that krylov subspace iterative methods for nonsymmetric systems display rates of convergence that are independent of the mesh parameter in addition we show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner

a descriptor system approach to non fragile h control for uncertain fuzzy neutral systems in this paper the problem of non fragile h control for a class of uncertain takagi sugeno t s fuzzy neutral systems with linear fractional parametric uncertainties is considered the non fragile h control problem is to design a state feedback controller with parameter uncertainties such that the l 2 induced gain of the mapping from the exogenous input to the controlled output is less than some prescribed level based on lyapunov krasovskii functional the descriptor model transformation and lmi approach new sufficient conditions for solvability of this problem are obtained it is shown that by a novel controller design method the desired state feedback fuzzy controller can be constructed by solving a set of lmis and the minimum h disturbance attenuation level can be obtained via using the lmi algorithm mincx finally an illustrative numerical example is provided to demonstrate correctness and effectiveness of the theoretical results

two sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices abstract in this paper we investigate and analyze in detail the structure and properties of a simultaneous decomposition for fifteen matrices a i c p i t i b i c s i q i c i c p i t i 1 d i c s i 1 q i and e i c p i q i i 1 2 3 we show that from this simultaneous decomposition we can derive some necessary and sufficient conditions for the existence of a solution to the system of two sided coupled generalized sylvester matrix equations with four unknowns a i x i b i c i x i 1 d i e i i 1 2 3 apart from proving an expression for the general solutions to this system we derive the range of ranks of these solutions using the ranks of the given matrices a i b i c i d i and e i we provide some numerical examples to illustrate our results moreover we present a similar approach to consider the simultaneous decomposition for 5k matrices and the system of k two sided coupled generalized sylvester matrix equations with k 1 unknowns a i x i b i c i x i 1 d i e i i 1 k k 4 the main results are also valid over the real number field and the real quaternion algebra

squaring down by static and dynamic compensators given a system which is not necessarily invertible and which has an unequal number of inputs a method of squaring down that is a method of designing pre compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible is presented the compensators are in general dynamic and have the property that the additional finite zeros induced by them are assignable to the open left half complex plan furthermore the compensators are asymptotically stable and hence do not deteriorate the robustness and performance of an eventual feedback design also the compensator design preserves the stabilizability detectability and minimum phase properties and the infinite zero structure of the original system thus a method of designing nonsquare systems by converting them to square invertible systems is introduced two applications of such a design philosophy 1 diagonal decoupling with state feedback and 2 almost disturbance decoupling with output feedback are pointed out

necessary and sufficient conditions for zero assignment by constant squaring down the problem of zero assignment by constant squaring down czap is studied for minimal systems described by a transfer function g s rm l s m l using tools from exterior algebra and algebraic geometry conditions for its solvability are given in terms of the numbers m l the forney dynamical order and the rank of the plucker matrix p for the cases l 1 or l m 1 it is shown that g s is completely zero assignable cza if and only if 1 for the cases l 1 m 1 it is proved that g s is cza or generically zero assignable gza under a complex squaring down if and only if l m l 1 and 1 the latter conditions also provide necessary conditions for the existence of a real solution for a generic g s sufficient conditions for solvability of czap by a real squaring down are that l m l 1 and that the number g a0 al 1 1 a0 al 1 i j ai aj is odd for some set a0 al 1 satisfying 1 l 1i 0ai l l 1 2 and 0 a0 a1 al 1 m 1 apart from the existence results the present approach also allows the computation of the solutions whenever they exist finally it is proved that the only fixed zeros of czap are the zeros of g s and a procedure for computing the solutions of czap whenever such solutions exist based on an optimization problem is given

some sufficient conditions for exponential stability of linear neutral functional differential equations abstract in this paper we give some sufficient conditions for exponential stability of linear neutral functional differential equations the obtained results are extensions of the recent results in d q cao p he stability criteria of linear neutral systems with a single delay appl math comput 148 2004 135 143 d q cao p he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu x f zou stability of linear neutral systems with multiple delays boundary criteria appl math comput 148 2004 707 715 j h park s won a note on stability of neutral delay differential systems j franklin inst 336 1999 1 9 to linear neutral functional differential equations

decentralized determinantal assignment problem fixed and almost fixed modes and zeros the decentralized determinantal assignment problem ddap is defined as the unifying description for the study of pole and zero assignment problems under decentralized output state feedback dof dsf and decentralized squaring down dsd respectively ddap is reduced to a linear problem of zero assignment of polynomial combinants and a multilinear problem of restricted decomposability of multivectors the decentralization characteristic dc and the decentralized polynomial grassmann representative d s gr of ddap are defined the fixed zero polynomial of ddap is then determined as the zero polynomial of d s gr the canonical d s gr cd r s gr and the decentralized plucker matrix dpm of ddap are introduced and necessary conditions for arbitrary assignment of the non fixed zeros are given in terms of the dpm the family of strongly zero non assignable sna systems is defined and for such systems the notion of the fixed zero is extended to that of the almost fixed zero afz an

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

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

a domain decomposition method with lagrange multipliers and inexact solvers for linear elasticity a new domain decomposition method with lagrange multipliers for elliptic problems is introduced it is based on a reformulation of the well known finite element tearing and interconnecting feti method as a saddle point problem with both primal and dual variables as unknowns the resulting linear system is solved with block structured preconditioners combined with a suitable krylov subspace method this approach allows the use of inexact subdomain solvers for the positive definite subproblems it is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems numerical results are presented for a plane stress cantilever membrane problem

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

threshold incomplete factorization constraint preconditioners for saddle point matrices abstract this paper presents a drop threshold incomplete ld 1lt factorization constraint preconditioner for saddle point systems using a threshold parameter a transformed saddle point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting a priori pivots based on these pivots an incomplete ld 1lt factorization constraint preconditioner is computed that approaches an exact form as approaches zero we prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors numerical results are presented for validation

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

numerical methods for fully nonlinear elliptic equations of the monge ampere type abstract in this article we discuss the numerical solution of the dirichlet problem for the monge ampere equation in two dimensions the solution of closely related problems is also discussed these include a family of pucci s equations the equation prescribing the harmonic mean of the eigenvalues of the hessian of a smooth function of two variables and a minimization problem from nonlinear elasticity where the cost functional involves the determinant of the gradient of vector valued functions to solve the monge ampere equation we consider two methods the first one reduces the monge ampere equation to a saddle point problem for a well chosen augmented lagrangian to solve this saddle point problem we advocate an uzawa douglas rachford algorithm the second method combines nonlinear least squares and operator splitting this second method being simpler to implements we apply variants of it to the solution of the other problems for the space discretization we use mixed finite element approximations closely related to methods already used for the solution of linear and nonlinear bi harmonic problems through these approximations the solution of the above problems is essentially reduced to the solution of discrete poisson problems the methods discussed in this article are validated by the results of numerical experiments

a least squares method for the inverse reflector problem in arbitrary orthogonal coordinates abstract in this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far field of the reflector by use of a least squares method we derive the monge ampere equation expressing conservation of energy while assuming an arbitrary coordinate system we generalize a cartesian coordinate least squares method presented earlier by prins et al 13 to arbitrary orthogonal coordinate systems this generalized least squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source this results in significantly increased numerical accuracy decrease of errors by factors up to 104 is reported we present the generalized least squares method and compare its numerical results with the cartesian version for a disk shaped light source

an improved delay dependent stability criterion for linear uncertain systems with multiple time varying delays in this paper the problem of delay dependent robust stability for a class of linear uncertain systems with multiple time varying delays is investigated a new multiple time varying delays criterion for improving the delay dependent robust stability in the form linear matrix inequalities is proposed using the augmented lyapunov krasovskii functional and jensen s inequality the result enlarges the existing maximum allowable bound of the time delay furthermore we theoretically consider the relationship of the maximum allowable delay bound of each time varying delay to reduce the conservatism an illustrative example is given to show the efficacy of the obtained result

a lagrangian scheme for the solution of the optimal mass transfer problem a lagrangian method to numerically solve the l 2 optimal mass transfer problem is presented the initial and final density distributions are approximated by finite mass particles having a gaussian kernel mass conservation and the hamilton jacobi equation for the potential are identically satisfied by constant mass transport along straight lines the scheme is described in the context of existing methods to solve the problem and a set of numerical examples including applications to medical imagery are presented

an algorithm for computing state feedback in multiinput linear systems a new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems the algorithm has good numerical behavior it also allows the user to adjust the eigenstructure of the resulting feedback system and therefore improve the condition of the problem and computation

a numerical method for the elliptic monge ampere equation with transport boundary conditions the problem of optimal mass transport arises in numerous applications including image registration mesh generation reflector design and astrophysics one approach to solving this problem is via the monge ampere equation while recent years have seen much work in the development of numerical methods for solving this equation very little has been done on the implementation of the transport boundary condition in this paper we propose a method for solving the transport problem by iteratively solving a monge ampere equation with neumann boundary conditions to enable mappings between variable densities we extend an earlier discretization of the equation to allow for right hand sides that depend on gradients of the solution b d froese and a m oberman siam j numer anal 49 2011 pp 1692 1714 this discretization provably converges to the viscosity solution the resulting system is solved efficiently with newton s method we provide several challenging computational examples that demonstra

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

on block preconditioners for nonsymmetric saddle point problems we discuss a class of preconditioning methods for an iterative solution of algebraic nonsymmetric saddle point problems arising from a mixed finite element discretization of partial differential equations in particular the navier stokes equation we prove that block diagonal and block triangular preconditioners based on symmetric positive definite blocks guarantee that the convergence rate of the method is independent of the mesh parameter h

data driven optimal transport the problem of optimal transport between two distributions x and y is extended to situations where the distributions are only known through a finite number of samples xi and yj a weak formulation is proposed based on the dual of the kantorovich formulation with two main modifications replacing the expected values in the objective function by their empirical means over the xi and yj and restricting the dual variables u x and v y to a suitable set of test functions adapted to the local availability of sample points a procedure is proposed and tested for the numerical solution of this problem based on a fluidlike flow in phase space where the sample points play the role of active lagrangian markers 2016 wiley periodicals inc

coping with model error in variational data assimilation using optimal mass transport classical variational data assimilation methods address the problem of optimally combining model predictions with observations in the presence of zero mean gaussian random errors however in many natural systems uncertainty in model structure and or model parameters often results in systematic errors or biases prior knowledge about such systematic model error for parametric removal is not always feasible in practice limiting the efficient use of observations for improved prediction the main contribution of this work is to advocate the relevance of transportation metrics for quantifying nonrandom model error in variational data assimilation for nonnegative natural states and fluxes transportation metrics also known as wasserstein metrics originate in the theory of optimal mass transport omt and provide a nonparametric way to compare distributions which is natural in the sense that it penalizes mismatch in the values and relative position of masses in the two distributions we demonstrate the promise of the proposed methodology using 1 d and 2 d advection diffusion dynamics with systematic error in the velocity and diffusivity parameters moreover we combine this methodology with additional regularization functionals such as the l1 norm of the state in a properly chosen domain to incorporate both model error and potential prior information in the presence of sparsity or sharp fronts in the underlying state of interest

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

stability criteria of linear neutral systems with a single delay this article studies the asymptotic stability of linear neutral delay differential systems using the characteristic equation of the system new simple delay independent stability criteria are derived in terms of the spectral radius of modulus matrices numerical examples are given to demonstrate the validity of our main criteria

numerical solution of the optimal transportation problem using the monge ampere equation a numerical method for the solution of the elliptic monge ampere partial differential equation with boundary conditions corresponding to the optimal transportation ot problem is presented a local representation of the ot boundary conditions is combined with a finite difference scheme for the monge ampere equation email protected s method is implemented leading to a fast solver comparable to solving the laplace equation on the same grid several times theoretical justification for the method is given by a convergence proof in the companion paper 4 solutions are computed with densities supported on non convex and disconnected domains computational examples demonstrate robust performance on singular solutions and fast computational times

explanation of variability and removal of confounding factors from data through optimal transport a methodology based on the theory of optimal transport is developed to attribute variability in data sets to known and unknown factors and to remove such attributable components of the variability from the data denoting by x the quantities of interest and by z the explanatory factors the procedure transforms x into filtered variables y through a z dependent map so that the conditional probability distributions x z are pushed forward into a target distribution y independent of z among all maps and target distributions that achieve this goal the procedure selects the one that minimally distorts the original data the barycenter of the x z connections are found to unsupervised learning and to fundamental problems in statistics such as conditional density estimation and sampling particularly simple instances of the methodology are shown to be equivalent to k means and principal component analysis an application is shown to a time series of ground temperature hourly data across the united states 2017 wiley periodicals inc

optimal transport for particle image velocimetry particle image velocimetry piv is a method used to measure the velocity field of a fluid flow traditionally cross correlation algorithms are used to retrieve the flow velocity recently a new method for piv based on the l 2 optimal mass transportation problem ot piv was introduced and analyzed in l p saumier b khouider and m agueh comm math sci 13 2015 pp 269 296 for the case of synthetically generated data and for particles of equal mass or brightness here we extend the work of saumier et al to the case of particles with different masses and randomly seeded particles more importantly we compare the ot piv method with a typical cross correlation algorithm for the case of real data using a combination of theory and numerical experiments we demonstrate that in the presence of particles with different weights brightness the ot method is more accurate for the largest brightest particles and it is more faithful when the particles are far enough from each other this makes it more suitable for the so called particle tracking regime of piv i e when the seeding density is low we demonstrate in particular that for low seeding densities the ot method performs better than a typical cross correlation algorithm based on these new results and the previous ones of saumier et al we propose a suite of postprocessing algorithms for the ot piv method it is found that the ot piv with postprocessing performs very well on the synthetic and real data when compared to the cross correlation method

brief paper further results on structural assignment of linear systems via sensor selection the problem of assigning structural properties of a linear system through sensor selection is for a given pair a b to find an output pair c d such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures and the invertibility properties in this paper by introducing the notion of infinite zero assignable sets for the pair a b we establish necessary and sufficient conditions for the assignability of a given set of infinite zeros and a set of structural properties which includes the left invertibility property in establishing these conditions we develop a numerical algorithm for the construction of the required c d

performance and analysis of saddle point preconditioners for the discrete steady state navier stokes equations we examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady state navier stokes equations with a combination of analytic and empirical results we study the effects of fundamental parameters on convergence we demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers the structure of these distributions is independent of the discretization mesh size but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller these characteristics are directly correlated with the convergence properties of iterative solvers

mesh independence for an augmented lagrangian sqp method in hilbert spaces an augmented lagrangian sqp algorithm for optimal control of differential equations in hilbert spaces is analyzed this algorithm has second order convergence rate provided that a second order sufficient optimality condition is satisfied the internal approximation of this method is investigated and convergence results are presented a mesh independence principle for the augmented lagrangian sqp method is proved which asserts that asymptotically the infinite dimensional algorithm and finite dimensional discretizations have the same convergence property more precisely for sufficiently small mesh size there is at most a difference of one iteration step between the number of steps required by the infinite dimensional method and its discretization to converge within a given tolerance varepsilon 0 the theoretical results are demonstrated by two optimal control problems for the burgers equation

computational design techniques for reduced order compensators the authors propose two computational techniques for the pole placement problem using reduced order compensators computationally efficient algorithms are presented for the observer based compensator and the brasch pearson compensator the key tool for these algorithms is the concept of two coupled sylvester equations the solutions of which completely characterize the desired reduced order compensators

synchronization of markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time varying delays the paper investigates the synchronization stability problem for a class of complex dynamical networks with markovian jumping parameters and mixed time delays the complex networks consist of m modes and the networks switch from one mode to another according to a markovian chain with known transition probability the mixed time delays are composed of discrete and distributed delays the discrete time delay is assumed to be random and its probability distribution is known a priori in terms of the probability distribution of the delays the new type of system model with probability distribution dependent parameter matrices is proposed based on the stochastic analysis techniques and the properties of the kronecker product delay dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159