a fixed point iteration approach for multibody dynamics with contact and small friction acceleration force setups for multi rigid body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients a painleve paradox this difficulty is circumvented by time stepping methods using impulse velocity approaches which solve complementarity problems with possibly nonconvex solution sets we show that very simple configurations involving two bodies may have a nonconvex solution set for any nonzero value of the friction coefficient we construct two fixed point iteration algorithms that solve convex subproblems and that are guaranteed for sufficiently small friction coefficients to retrieve at a linear convergence rate the unique velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled in addition we show that one step of one of the iterative algorithms provides an excellent approximation to the velocity solution of the original possibly nonconvex problem if for all contacts we have that either the friction coefficient is small or the slip velocity is small

recurrent neural network for computing the drazin inverse this paper presents a recurrent neural network rnn for computing the drazin inverse of a real matrix in real time this recurrent neural network rnn is composed of n independent parts subnetworks where n is the order of the input matrix these subnetworks can operate concurrently so parallel and distributed processing can be achieved in this way the computational advantages over the existing sequential algorithms can be attained in real time applications the rnn defined in this paper is convenient for an implementation in an electronic circuit the number of neurons in the neural network is the same as the number of elements in the output matrix which represents the drazin inverse the difference between the proposed rnn and the existing ones for the drazin inverse computation lies in their network architecture and dynamics the conditions that ensure the stability of the defined rnn as well as its convergence toward the drazin inverse are considered in addition illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network

nonlinear second order elliptic equations v the dirichlet problem for weingarten hypersurfaces on etudie le probleme de dirichlet pour une fonction u dans un domaine borne de r n a frontiere lisse strictement convexe en un point x de les courbures principales k k 1 k n du graphe x u x satisfont une relation f k 1 k n x 0 ou est une fonction positive lisse donnee sur de plus u doit satisfaire la condition aux limites de dirichlet u 0 sur sous certaines conditions on demontre qu il existe une solution u unique admissible lisse dans

singular sets for curvature equation of order k abstract we consider the removability of singular sets for the curvature equations of the form h k u which is determined by the kth elementary symmetric function in an n dimensional domain we prove that for 1 k n 1 and a compact set k whose n k dimensional hausdorff measure is zero any generalized solution to the curvature equation on k is always extendable to a generalized solution on the whole domain

exploiting hessian matrix and trust region algorithm in hyperparameters estimation of gaussian process gaussian process gp regression is a bayesian non parametric regression model showing good performance in various applications however it is quite rare to see research results on log likelihood maximization algorithms instead of the commonly used conjugate gradient method the hessian matrix is first derived simplified in this paper and the trust region optimization method is then presented to estimate gp hyperparameters numerical experiments verify the theoretical analysis showing the advantages of using hessian matrix and trust region algorithms in the gp context the trust region optimization method is a robust alternative to conjugate gradient method also in view of future researches on approximate and or parallel gp implementation

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

recurrent neural network approach based on the integral representation of the drazin inverse in this letter we present the dynamical equation and corresponding artificial recurrent neural network for computing the drazin inverse for arbitrary square real matrix without any restriction on its eigenvalues conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the drazin inverse are considered several illustrative examples present the results of computer simulations

generalized solutions of curvature equations abstract we introduce a notion of generalized solutions for the so called curvature equations it is an extension of the definition of generalized solutions of the gauss curvature equation and gives a new framework for the study of more general curvature equations we prove that if the curvature equation has a convex solution then the inhomogeneous term must be a borel measure we also discuss basic properties of generalized solutions among other things we show that our class of generalized solutions is wider than that of weak solutions

minimizing quadratic functions with semidefinite hessian subject to bound constraints the mprgp modified proportioning with reduced gradient projections algorithm for minimization of the strictly convex quadratic function subject to bound constraints is adapted to the solution of problems with a semidefinite hessian a the adapted algorithm accepts the decrease directions that belong to the null space of a and generates the iterates that are proved to minimize the cost function the paper examines specific features of the solution of the problems with convex but not necessarily strictly convex hessian the performance of the algorithm is demonstrated by the solution of a semi coercive contact problem of elasticity and a 3d particle dynamics problem the results are compared with those obtained by the spectral projected gradient method and the projected jacobi method

regularized image reconstruction using svd and a neural network method for matrix inversion two methods of matrix inversion are compared for use in an image reconstruction algorithm the first is based on energy minimization using a hopfield neural network this is compared with the inverse obtained using singular value decomposition svd it is shown for a practical example that the neural network provides a more useful and robust matrix inverse

global exponential convergence and stability of gradient based neural network for online matrix inversion wang proposed a gradient based neural network gnn to solve online matrix inverses global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices as compared to the previously presented asymptotical convergence this paper investigates more desirable properties of the gradient based neural network e g global exponential convergence for nonsingular matrix inversion and global stability even for the singular matrix case illustrative simulation results further demonstrate the theoretical analysis of gradient based neural network for online matrix inversion

neural network approach for solving nonsingular multi linear tensor systems abstract the main propose of this paper is to develop two neural network models for solving nonsingular multi linear tensor system theoretical analysis shows that each of the neural network models ensures the convergence performance for possible hardware implementation of the proposed neural network models based on digital circuits we adopt the euler type difference rule to discretize the corresponding gradient neural network gnn models the computer simulation results further substantiate that the models can solve a multi linear system with nonsingular tensors

using krylov subspace and spectral methods for solving complementarity problems in many body contact dynamics simulation summary many body dynamics problems are expected to handle millions of unknowns when for instance investigating the three dimensional flow of granular material unfortunately the size of the problems tractable by existing numerical solution techniques is severely limited on convergence grounds this is typically the case when the equations of motion embed a differential variational inequality problem that captures contact and possibly frictional interactions between rigid and or flexible bodies as the size of the physical system increases the speed and or the quality of the numerical solution decreases this paper describes three methods the gradient projected minimum residual method the preconditioned spectral projected gradient with fallback method and the modified proportioning with reduced gradient projection method that demonstrate better scalability than the projected jacobi and gauss seidel methods commonly used to solve contact problems that draw on a differential variational inequality based modeling approach copyright 2013 john wiley sons ltd

isolated singularities for some types of curvature equations abstract we consider the removability of isolated singularities for the curvature equations of the form h k u 0 which is determined by the k th elementary symmetric function in an n dimensional domain we prove that for 1 k n 1 isolated singularities of any viscosity solutions to the curvature equations are always removable provided the solution can be extended continuously at the singularities we also consider the class of generalized solutions and prove the removability of isolated singularities

complex valued zhang neural network for online complex valued time varying matrix inversion abstract in this paper a new complex valued recurrent neural network cvrnn called complex valued zhang neural network cvznn is proposed and simulated to solve the complex valued time varying matrix inversion problems such a cvznn model is designed based on a matrix valued error function in the complex domain and utilizes the complex valued first order time derivative information of the complex valued time varying matrix for online inversion superior to the conventional complex valued gradient based neural network cvgnn and its related methods the state matrix of the resultant cvznn model can globally exponentially converge to the theoretical inverse of the complex valued time varying matrix in an error free manner moreover by exploiting the design parameter 1 superior convergence can be achieved for the cvznn model to solve such complex valued time varying matrix inversion problems as compared with the situation without design parameter involved i e the situation with 1 computer simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a cvznn model for online complex valued time varying matrix inversion

recurrent implicit dynamics for online matrix inversion a novel kind of recurrent implicit dynamics together with its electronic realization is proposed and exploited for real time matrix inversion compared to conventional explicit neural dynamics our proposed model in the form of implicit dynamics has the following advantages a can coincide better with systems in practice and b has higher abilities in representing dynamic systems more importantly our model can achieve superior convergence performance in comparison with the existing dynamic systems specifically gradient based dynamics gd and recently proposed zhang dynamics zd theoretical analysis and computer simulation results substantiate the effectiveness and superior efficiency of our model for online matrix inversion

different stochastic algorithms to obtain matrix inversion in this paper we present different monte carlo algorithms to obtain inverse matrix here we first determine two algorithms and describe their restrictions to be applicable for computing the inversion of a nonsingular matrix then we establish an efficient algorithm to obtain approximate inversion of an arbitrary nonsingular matrix this algorithm obtain an accurate inversion when the other two algorithm are broken down finally we compare the performances of third algorithm with two previous algorithms

hessian measures ii in our previous paper on this topic we introduced the notion of k hessian measure associated with a continuous k convex function in a domain q in euclidean n space k 1 n and proved a weak continuity result with respect to local uniform convergence in this paper we consider k convex functions not necessarily continuous and prove the weak continuity of the associated k hessian measure with respect to convergence in measure the proof depends upon local integral estimates for the gradients of k convex functions

survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems

compactness theorems for differential forms we prove compactness properties of various sets of differential forms with bounds on their exterior derivatives this gives simple proofs of the federer fleming result on normal currents and of compensated compactness lemmas

a systolic architecture for fast dense matrix inversion an array that inverts an n n dense matrix in 5n 1 time units including i o time is presented the inversion algorithm consists of three phases and assumes that gaussian elimination without pivoting can be applied the array which consists of 2n sup 2 n simple processing elements implements and overlaps the execution of all three phases without any need for intermediate i o or reconfiguration an efficient data steering technique which is well suited for feedback recurrences is utilized