multisymplectic geometry and multisymplectic preissman scheme for the kp equation the multisymplectic structure of the kp equation is obtained directly from the variational principal using the covariant de donder weyl hamilton function theories we reformulate the kp equation to the multisymplectic form which was proposed by bridges from the multisymplectic equation we can derive a multisymplectic numerical scheme of the kp equation which can be simplified to the multisymplectic 45 points scheme

backward error analysis for multi symplectic integration methods a useful method for understanding discretization error in the numerical solution of odes is to compare the system of odes with the modified equations obtained through backward error analysis and using symplectic integration for hamiltonian odes provides more incite into the modified equations in this paper the ideas of symplectic integration are extended to hamiltonian pdes and this paves the way for the development of a local modified equation analysis solely as a useful diagnostic tool for the study of these types of discretizations in particular local conservation laws of energy and momentum are not preserved exactly when symplectic integrators are used to discretize but the modified equations are used to derive modified conservation laws that are preserved to higher order along the numerical solution these results are also applied to the nonlinear wave equation

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

the midpoint scheme and variants for hamiltonian systems advantages and pitfalls the implicit midpoint scheme like higher order gauss collocation schemes is algebraically stable and symplectic and it preserves quadratic integral invariants it may appear particularly suitable for the numerical solution of highly oscillatory hamiltonian systems such as those arising in molecular dynamics or structural mechanics because there is no stability restriction when it is applied to a simple harmonic oscillator although it is well known that the midpoint scheme may also exhibit instabilities in various stiff situations one might still hope for good results when resonance type instabilities are avoided in this paper we investigate the suitability of the midpoint scheme for highly oscillatory frictionless mechanical systems where the step size k is much larger than the system s small parameter varepsilon in the case that the solution remains bounded as varepsilon rightarrow 0 we show that in general one must require that k 2 varepsilon be small enough or else even the errors in slowly varying quantities like the energy may grow undesirably especially when fast and slow modes are tightly coupled or worse the computation may yield misleading information in some cases this may already happen when k o varepsilon the same holds for higher order collocation at gaussian points the encountered restrictions on k are typically still better than the corresponding ones for explicit schemes

construction of multisymplectic schemes of any finite order for modified wave equations in this paper we analyze several symplectic discretizations of linear wave equations with periodic boundary conditions and show the discretizations are multisymplectic of arbitrary finite order for wave equations when the periodic boundary condition vanishes

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

maximum likelihood image matching image matching applications such as tracking and stereo commonly use the sum of squared difference ssd measure to determine the best match however this measure is sensitive to outliers and is not robust to template variations alternative measures have also been proposed that are more robust to these issues we improve upon these using a probabilistic formulation for image matching in terms of maximum likelihood estimation that can be used for both edge template matching and gray level image matching this formulation generalizes previous edge matching methods based on distance transforms we apply the techniques to stereo matching and feature tracking uncertainty estimation techniques allow feature selection to be performed by choosing features that minimize the localization uncertainty

explicit lie poisson integration and the euler equations we give a wide class of lie poisson systems for which explicit lie poisson integrators preserving all casimirs can be constructed the integrators are extremely simple and have widespread applicability examples are the free rigid body a moment truncation and a new fast algorithm for the sine bracket truncation of the 2d euler equations

symplectic energy momentum preserving variational integrators the purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving to do this a space time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy criteria for the solvability of the time steps and some numerical examples are given

feedback control of two time scale block implemented discrete time systems the block processing technique is applied to a class of two time scale linear discrete time systems block state space structures for slow and fast subsystems have been obtained based upon these models blocked slow and fast controls are designed in addition an extra control is designed to exactly compensate for the effects of the parasitics

parallel and sequential block kalman filtering and their implementations using systolic arrays two sets of block kalman filtering equations that differ in the manner of generating the initial and updated estimates are derived parallel and sequential schemes for generating these estimates are adopted it is shown that the parallel implementation inherently leads to a block kalman estimator which provides filtered estimates at the vector block level and fixed lag smoother estimates at the sample level the sequential implementation scheme on the other hand generates the estimates of each sample recursively leading naturally to a scalar filter estimator these scalar estimates are arranged in a vector form resulting in a block estimator which solely generates filtered estimates both at the vector and sample levels simulation results on a speech signal are presented which indicate the advantages of the sequential block kalman filter an algorithm for iterative calculation of kalman gain and error covariance matrices is given which does not require any matrix inversion operation the implementation of this algorithm using available systolic array processors is presented a ring systolic array which can be used to implement the state update part of the block kalman filter is suggested

local discontinuous galerkin methods for the kuramoto sivashinsky equations and the ito type coupled kdv equations in this paper we develop a local discontinuous galerkin method to solve the kuramoto sivashinsky equations and the ito type coupled kdv equations the l2 stability of the schemes is obtained for both of these nonlinear equations we use both the traditional nonlinearly stable explicit high order runge kutta methods and the explicit exponential time differencing method for the time discretization the latter can achieve high order accuracy and maintain good stability while avoiding the very restrictive explicit stability limit of the former when the pde contains higher order spatial derivatives numerical examples are shown to demonstrate the accuracy and capability of these methods

multi symplectic runge kutta collocation methods for hamiltonian wave equations a number of conservative pdes like various wave equations allow for a multi symplectic formulation which can be viewed as a generalization of the symplectic structure of hamiltonian odes we show that gauss legendre collocation in space and time leads to multi symplectic integrators i e to numerical methods that preserve a symplectic conservation law similar to the conservation of symplecticity under a symplectic method for hamiltonian odes we also discuss the issue of conservation of energy and momentum since time discretization by a gauss legendre method is computational rather expensive we suggest several semi explicit multi symplectic methods based on gauss legendre collocation in space and explicit or linearly implicit symplectic discretizations in time

nonuniform filter bank design with noises this work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise three main nonuniform filter bank systems i e filter block decimator fbd structure upsampler filter downsampler ufd structure and tree structure are included in this study according to different operating conditions two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed respectively at the first stage a unified block state space model for different nonuniform filter bank systems with noise is developed then by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable if the input signal is lacking in modeling the signal reconstruction is discussed from the minimax estimation point of view two state estimation techniques involving robust kalman filtering and h sub spl infin filtering are employed respectively to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal finally several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances

estimation and identification for 2 d block kalman filtering the development of a recursive identification and estimation procedure for two dimensional block kalman filtering is discussed the recursive identification scheme can be used online to update the image model parameters at each iteration based on the local statistics within a block of the observed noisy image the covariance matrix of the driving noise can also be estimated at each iteration of this algorithm a recursive procedure for computing the parameters of the higher order models is given simulation results are also provided

a mixed algorithm for numerical computation of soliton solutions of the coupled kdv equation finite difference method and differential quadrature method abstract the aim of the manuscript is to investigate numerical solutions of the system of coupled korteweg de vries equation for this approximation we have used finite difference method for time integration and differential quadrature method depending on modified cubic b splines for space integration to display the accuracy of the present mixed method three famous test problems namely single soliton interaction of two solitons and birth of solitons are solved and the error norms l2 and l are computed and compared with earlier works comparison of error norms show that present mixed method obtained superior results than earlier works by using same parameters and less number of nodal points at the same time two lowest invariants and amplitude values of solitons during the simulations are calculated and reported in addition those relative changes of invariants are computed and tabulated properties of solitons observed clearly at the all of the test problems and figures of the all of the simulations are given

stability and instability of solitary waves of the fifth order kdv equation a numerical framework abstract the spectral problem associated with the linearization about solitary waves of the generalized fifth order kdv equation is formulated in terms of the evans function a complex analytic function whose zeros correspond to eigenvalues a numerical framework based on a fast robust shooting algorithm on exterior algebra spaces is introduced the complete algorithm has several new features including a rigorous numerical algorithm for choosing starting values a new method for numerical analytic continuation of starting vectors the role of the grassmannian g 2 c 5 in choosing the numerical integrator and the role of the hodge star operator for relating 2 c 5 and 3 c 5 and deducing a range of numerically computable forms for the evans function the algorithm is illustrated by computing the stability and instability of solitary waves of the fifth order kdv equation with polynomial nonlinearity

verlet i r respa impulse is limited by nonlinear instabilities this paper shows that in molecular dynamics md when constant energy nve simulations of newton s equations of motion are attempted using the multiple time stepping mts integrator verlet i r respa impulse there are nonlinear instabilities when the longest step size is a third or possibly a fourth of the period s of the fastest motion s in the system this is demonstrated both through a thorough set of computer experiments and through the analysis of a nonlinear model problem the numerical experiments include not only the unconstrained dynamics simulation of a droplet of flexible water and a flexible protein but also the constrained dynamics simulation of a solvated protein representing a range of simulation protocols commonly in use by biomolecular modelers the observed and predicted instabilities match exactly previous work has identified and explained a linear instability for verlet i r respa impulse at around half the period of the fastest motion mandziuk and schlick discovered nonlinear resonances in single time stepping md integrators but unstable nonlinear resonances for mts integrators are reported here for the first time this paper also offers an explanation on the instability of mts constrained molecular dynamics simulations of explicitly solvated proteins more aggressive multiple step sizes are possible with mild langevin coupling or targeted langevin coupling and its combination with the mollified impulse method permits step sizes 3 to 4 times larger thanverlet i r respa impulse while still retaining some accuracy

tracking non rigid objects using probabilistic hausdorff distance matching this paper proposes a new method of extracting and tracking a non rigid object moving against a cluttered background while allowing camera movement for object extraction we first detect an object using watershed segmentation technique and then extract its contour points by approximating the boundary using the idea of feature point weighting for object tracking we take the contour to estimate its motion in the next frame by the maximum likelihood method the position of the object is estimated using a probabilistic hausdorff measurement while the shape variation is modelled using a modified active contour model the proposed method is highly tolerant to occlusion unless an object is fully occluded during tracking the result is stable and the method is robust enough for practical application

a statistical approach to sparse multi scale phase based stereo in this study a multi scale phase based sparse disparity algorithm and a probabilistic model for matching uncertain phase are proposed the features used are oriented edges extracted using steerable filters feature correspondences are estimated using phase similarity at multiple scale using a magnitude weighting scheme in order to achieve sub pixel accuracy in disparity we use a fine tuning procedure which employs the phase difference between corresponding feature points we also derive a probabilistic model where phase uncertainty is trained using data from a single image pair the model is used to provide stable matches the disparity algorithm and the probabilistic phase uncertainty model are verified on various stereo image pairs

multisymplectic geometry and multisymplectic preissmann scheme for the kdv equation the multisymplectic structure of the kdv equation is presented directly from the variational principle from the numerical view point we give a multisymplectic twelve points scheme which is equivalent to the multisymplectic preissmann scheme finally we test the twelve points scheme on solitary waves over long time intervals

multi symplectic methods for the ito type coupled kdv equation abstract in this paper we find that the ito type coupled kdv equation can be written as a multi symplectic hamiltonian partial differential equation pde then multi symplectic fourier pseudospectral method and multi symlpectic wavelet collocation method are constructed for this equation in the numerical experiments we show the effectiveness of the proposed methods some comparisons between the proposed methods are also made with respect to global conservation properties

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

multisymplectic conservation laws for differential and differential difference equations many well known partial differential equations can be written as multisymplectic systems such systems have a structural conservation law from which scalar conservation laws can be derived these c

multi symplectic runge kutta methods for nonlinear dirac equations in this paper we consider the multi symplectic runge kutta msrk methods applied to the nonlinear dirac equation in relativistic quantum physics based on a discovery of the multi symplecticity of the equation in particular the conservation of energy momentum and charge under msrk discretizations is investigated by means of numerical experiments and numerical comparisons with non msrk methods numerical experiments presented reveal that msrk methods applied to the nonlinear dirac equation preserve exactly conservation laws of charge and momentum and conserve the energy conservation in the corresponding numerical accuracy to the method utilized it is verified numerically that msrk methods are stable and convergent with respect to the conservation laws of energy momentum and charge and msrk methods preserve not only the inner geometric structure of the equation but also some crucial conservative properties in quantum physics a remarkable advantage of msrk methods applied to the nonlinear dirac equation is the precise preservation of charge conservation law

backward error analysis for numerical integrators backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods this is true in particular for the integration of hamiltonian systems where backward error analysis can be used to show that a symplectic method will conserve energy over exponentially long periods of time such results are typically based on two aspects of backward error analysis i it can be shown that the modified vector fields have some qualitative properties which they share with the given problem and ii an estimate is given for the difference between the best interpolating vector field and the numerical method these aspects have been investigated recently for example by benettin and giorgilli in j statist phys 74 1994 pp 1117 1143 by hairer in ann numer math 1 1994 pp 107 132 and by hairer and lubich in numer math 76 1997 pp 441 462 in this paper we aim at providing a unifying framework and a simplification of the existing results and corresponding proofs our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit taylor series expansion of the numerical method and the corresponding flow maps as in the above cited works as an application we discuss the long time integration of chaotic hamiltonian systems and the approximation of time averages along numerically computed trajectories

symplectic wavelet collocation method for hamiltonian wave equations this paper introduces a novel symplectic wavelet collocation method for solving nonlinear hamiltonian wave equations based on the autocorrelation functions of daubechies compactly supported scaling functions collocation method is conducted for the spatial discretization which leads to a finite dimensional hamiltonian system then appropriate symplectic scheme is employed for the integration of the hamiltonian system under the hypothesis of periodicity the properties of the resulted space differentiation matrix are analyzed in detail conservation of energy and momentum is also investigated various numerical experiments show the effectiveness of the proposed method

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

natural discretizations for the divergence gradient and curl on logically rectangular grids abstract this is the first in series of papers creating a discrete analog of vector analysis on logically rectangular nonorthogonal nonsmooth grids we introduce notations for 2 d logically rectangular grids describe both cell valued and nodal discretizations for scalar functions and construct the natural discretizations of vector fields using the vector components normal and tangential to the cell boundaries we then define natural discrete analogs of the divergence gradient and curl operators based on coordinate invariant definitions and interpret these formulas in terms of curvilinear coordinates such as length of elements of coordinate lines areas of elements of coordinate surfaces and elementary volumes we introduce the discrete volume integral of scalar functions the discrete surface integral and a discrete analog of the line integral and prove discrete versions of the main theorems relating these objects these theorems include the following the discrete analog of relationship div a 0 if and only if a curl b curl a 0 if and only if a grad if a grad then the line integral does not depend on path and if the line integral of a vector function is equal to zero for any closed path then this vector is the gradient of a scalar function last we define the discrete operators div grad and curl in terms of primitive differencing operators based on forward and backward differences and primitive metric operators related to multiplications of discrete functions by length of edges areas of surfaces and volumes of 3 d cells these formulations elucidate the structure of the discrete operators and are useful when investigating the relationships between operators and their adjoints

high order multi symplectic schemes for the nonlinear klein gordon equation in this paper we construct multi symplectic schemes with any order of accuracy for the nonlinear klein gordon equation by concatenating the symplectic schemes for odes some existing schemes such as the preissman scheme and the leap frog scheme and new multi symplectic schemes are constructed we also show that the composition method which plays a crucial role in finding the high order symplectic integrators for the odes can also be applied to construct high order multi symplectic schemes for pdes extension of the concatenating method to more than one space dimension is also discussed numerical experiments are presented to show the order and the efficiency of the constructed multi symplectic schemes

the symplectic evans matrix and the instability of solitary waves and fronts hamiltonian evolution equations which are equivariant with respect to the action of a lie group are models for physical phenomena such as oceanographic flows optical fibres and atmospheric flows and such systems often have a wide variety of solitary wave or front solutions in this paper we present a new symplectic framework for analyzing the spectral problem associated with the linearization about such solitary waves and fronts at the heart of the analysis is a multi symplectic formulation of hamiltonian partial differential equations where a distinct symplectic structure is assigned for the time and space directions with a third symplectic structure with two form denoted by omega associated with a coordinate frame moving at the speed of the wave this leads to a geometric decomposition and symplectification of the evans function formulation for the linearization about solitary waves and fronts we introduce the concept of the symplectic evans matrix a matrix consisting of restricted omega symplectic forms by applying hodge duality to the exterior algebra formulation of the evans function we find that the zeros of the evans function correspond to zeros of the determinant of the symplectic evans matrix based on this formulation we prove several new properties of the evans function restricting the spectral parameter lambda to the real axis we obtain rigorous results on the derivatives of the evans function near the origin based solely on the abstract geometry of the equations and results for the large lambda behaviour which use primarily the symplectic structure but also extend to the non symplectic case the lie group symmetry affects the evans function by generating zero eigenvalues of large multiplicity in the so called systems at infinity we present a new geometric theory which describes precisely how these zero eigenvalues behave under perturbation by combining all these results a new rigorous sufficient condition for instability of solitary waves and fronts is obtained the theory applies to a large class of solitary waves and fronts including waves which are biasymptotic to a nonconstant manifold of states as x tends to infinity to illustrate the theory it is applied to three examples a boussinesq model from oceanography a class of nonlinear schrodinger equations from optics and a nonlinear klein gordon equation from atmospheric dynamics

geometric integrators for classical spin systems practical structure preserving methods for integrating classical heisenberg spin systems are discussed two new integrators are derived and compared including 1 a symmetric energy and spin length preserving integrator based on a red black splitting of the spin sites combined with a staggered timestepping scheme and 2 a lie poisson symplectic integrator based on hamiltonian splitting the methods are applied to both 1d and 2d lattice models and are compared with the commonly used explicit runge kutta projected runge kutta and implicit midpoint schemes on the bases of accuracy conservation of invariants and computational expense it is shown that while any of the symmetry preserving schemes improves the integration of the dynamics of solitons or vortex pairs compared to runge kutta or projected runge kutta methods the staggered red black scheme is far more efficient than the other alternatives

splitting multisymplectic integrators for maxwell s equations in the paper we describe a novel kind of multisymplectic method for three dimensional 3 d maxwell s equations splitting the 3 d maxwell s equations into three local one dimensional lod equations then applying a pair of symplectic runge kutta methods to discretize each resulting lod equation it leads to splitting multisymplectic integrators we say this kind of schemes to be lod multisymplectic scheme lod ms the discrete conservation laws convergence dispersive relation dissipation and stability are investigated for the schemes theoretical analysis shows that the schemes are unconditionally stable non dissipative and of first order accuracy in time and second order accuracy in space as a reduction we also consider the application of lod ms to 2 d maxwell s equations numerical experiments match the theoretical results well they illustrate that lod ms is not only efficient and simple in coding but also has almost all the nature of multisymplectic integrators

fast fourier transform algorithms for linear estimation smoothing and riccati equations in the past two decades since the advent of kalman s recursive filter numerous algorithms for linear estimation have emerged most of these algorithms are recursive and rely on solving a riccati equation or equivalent recursive equations it will be shown how some of the classical problems such as linear smoothing riccati equations boundary value problems and recursive block filtering problems can be solved exactly by some new nonrecursive algorithms which are based on the fast fourier transform fft in the context of modern digital signal processing these algorithms have a highly parallel structure and are well suited for vlsi implementations

multi symplectic spectral discretizations for the zakharov kuznetsov and shallow water equations abstract the time evolution of multi symplectic pdes with periodic boundary conditions in one and two space dimensions is considered we introduce the idea of a multi symplectic fourier transform for systems on periodic domains leading to a semi discretization on fourier space and to the concept of multi symplecticity on fourier space the spatial discretization leads to a discrete lattice model with certain discrete conservation laws imposed on it a discrete wave model a by product of the semi discretization is that it leads automatically to a system of hamiltonian odes in time when truncated we show that the one dimensional shallow water equations and the two dimensional zakharov kuznetsov equation are multi symplectic and derive spectral discretizations for these systems and present numerical experiments

numerical implementation of the multisymplectic preissman scheme and its equivalent schemes we analyze the multisymplectic preissman scheme for the kdv equation with the periodic boundary condition and show that the unconvergence of the widely used iterative methods to solve the resulting nonlinear algebra system of the preissman scheme is due to the introduced potential function a artificial numerical condition is added to the periodic boundary condition the added boundary condition makes the numerical implementation of the multisymplectic preissman scheme practical and is proved not to change the numerical solutions of the kdv equation based on our analysis we derive some new schemes which are not restricted by the artificial boundary condition and more efficient than the preissman scheme because of less computing cost and less computer storages by eliminating the auxiliary variables we also derive two schemes for the kdv equation one is a 12 point scheme and the other is an 8 point scheme as the byproducts we present two new explicit schemes which are not multisymplectic but still have remarkable numerical stable property numerical experiments on soliton collisions are also provided to confirm our conclusion and to show the benefits of the multisymplectic schemes with comparison of the spectral method and zabusky kruskal scheme

efficiently locating objects using the hausdorff distance the hausdorff distance is a measure defined between two point sets here representing a model and an image the hausdorff distance is reliable even when the image contains multiple objects noise spurious features and occlusions in the past it has been used to search images for instances of a model that has been translated or translated and scaled by finding transformations that bring a large number of model features close to image features and vice versa in this paper we apply it to the task of locating an affine transformation of a model in an image this corresponds to determining the pose of a planar object that has undergone weak perspective projection we develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria we can also efficiently locate only the best transformation we discuss an implementation of this approach and present some examples of its use

view based recognition using an eigenspace approximation to the hausdorff measure view based recognition methods such as those using eigenspace techniques have been successful for a number of recognition tasks such approaches however are somewhat limited in their ability to recognize objects that are partly hidden from view or occur against cluttered backgrounds in order to address these limitations we have developed a view matching technique based on an eigenspace approximation to the generalized hausdorff measure this method achieves compact storage and fast indexing that are the main advantages of eigenspace view matching techniques while also being tolerant of partial occlusion and background clutter the method applies to binary feature maps such as intensity edges rather than directly to intensity images

the multi symplecticity of partitioned runge kutta methods for hamiltonian pdes in this article we consider partitioned runge kutta prk methods for hamiltonian partial differential equations pdes and present some sufficient conditions for multi symplecticity of prk methods of hamiltonian pdes

finite difference calculus invariant structure of a class of algorithms for the nonlinear klein gordon equation in a previous work the authors have presented a formalism for deriving systematically invariant symmetric finite difference algorithms for nonlinear evolution differential equations that admit conserved quantities this formalism is herein cast in the context of exact finite difference calculus the algorithms obtained from the proposed formalism are shown to derive exactly from discrete scalar potential functions using finite difference calculus in the same sense as that of the corresponding differential equation being derivable from its associated energy function a conserved quantity a clear ramification of this result is that the derived algorithms preserve certain discrete invariant quantities which are the consistent counterpart of the invariant quantities in the continuous case results on the nonlinear stability of a class of algorithms that are derived using the proposed formalism and that preserve energy or linear momentum are discussed in the context of finite difference calculus some

nonlinear stability analysis of area preserving integrators linear stability analysis is inadequate for integrators designed for nondissipative systems such as hamiltonian systems in which nonlinear effects are often decisive mathematical theory exists kam theory for rigorous analysis of small perturbations from equilibria but it needs to be expressed in a form that is more easily applicable to the study of area preserving maps we have pursued this obtaining a completely rigorous nonlinear stability analysis for elliptic equilibria based on the moser twist theorem and a result of cabral and meyer nonlinearity 12 1999 pp 1351 1362 together with the theory of normal forms for hamiltonian systems the result is a determination of necessary and sufficient conditions for stability these conditions are sharpened for the case of reversible maps and applied to the symplectic members of the newmark family of integrators which includes the leapfrog the implicit midpoint and the stormer cowell methods nonlinear stability limits are more severe than those of linear theory as an example the leapfrog scheme actually has a step size limitation of 71 of that predicted by linear analysis

multisymplectic box schemes for the complex modified korteweg de vries equation in this paper two multisymplectic integrators an eight point preissman box scheme and a narrow box scheme are considered for numerical integration of the complex modified korteweg de vries equation energy and momentum preservation of both schemes and their dispersive properties are investigated the performance of both methods is demonstrated through numerical tests on several solitary wavesolutions

on the stability of symplectic and energy momentum algorithms for non linear hamiltonian systems with symmetry abstract this paper presents a detailed comparison of two implicit time integration schemes for a simple non linear hamiltonian system with symmetry the motion of a particle in a central force field the goal is to establish analytical and numerical results pertaining to the stability properties of the implicit mid point rule the proto typical implicit symplectic method and a particular energy momentum conserving scheme and to compare the two schemes with respect to accuracy while all results presented herein are within the context of a simple model problem the problem was constructed so as to exhibit key features typical of more complex systems with symmetry such as those arising in non linear solid mechanics namely the presence of large and relatively slow overall motions together with high frequency internal motions