a modified broyden like quasi newton method for nonlinear equations abstract in this paper we introduce a modified broyden like quasi newton method for solving nonlinear equations which is an acceleration version of the broyden like method presented by li and fukushima 2000 we show that the proposed method has global and superlinear convergence properties we report some numerical results to show its efficiency

a shamanskii like self adaptive levenberg marquardt method for nonlinear equations abstract in this paper we are concerned with the shamanskii like self adaptive levenberg marquardt methods for nonlinear equations we consider two choices of levenberg marquardt parameter one of them is the standard self adaptive levenberg marquardt parameter the other is nonmonotone self adaptive levenberg marquardt parameter by using the nonmonotone technique of grippo lampariello and lucidi under the error bound condition which is weaker than nonsingularity we show that the shamanskii like self adaptive levenberg marquardt methods converge with q order m 1 numerical experiments show the new algorithms are efficient and promising

a two stage filter for smoothing multivariate noisy data on unstructured grids abstract experimental data as well as numerical simulations are very often affected by noise random fluctuations that distort the final output or the intermediate products of a numerical process in this paper a new method for smoothing data given on nonstructured grids is proposed it takes advantage of the smoothing properties of kernel weighted averaging and least squares techniques the weighted averaging is performed following a shepard like procedure where gaussian kernels are employed while least squares fitting is reduced to the use of very few basis functions so as to improve smoothness though at the price of interpolation accuracy once we have defined an n point grid and want to make a smoothed fit at a given grid point this method reduces to consideration of all m point stencils for a given value of m where m n that include that point and to make a least squares fitting for that particular point in each of those stencils finally the various results thus obtained are weight averaged the weights being inversely proportional to the distance of the point to the middle of the stencil then this process is repeated for all the grid points so as to obtain the smoothing of the input function though this method is generalized for the multivariate case one two and five dimensional test cases are shown as examples of the performance of this method

structure and stability of finite dimensional approximations for functional differential equations this paper deals with the structural and stability properties of the averaging approximation scheme for linear retarded functional differential equations both in the discrete and in the continuous time case the structure of the approximating systems is shown to be analogous to the structure of the underlying retarded equation moreover it is shown that the approximating systems are exponentially stable in a uniform sense if the original system is asymptotically stable

tensor methods for nonlinear equations a new class of methods for solving systems of nonlinear equations called tensor methods is introduced tensor methods are general purpose methods intended especially for problems where the jacobian matrix at the solution is singular or ill conditioned they base each iteration on a quadratic model of the nonlinear function the standard linear model augmented by a simple second order term the second order term is selected so that the model interpolates function values from several previous iterations as well as the current function value and jacobian the tensor method requires no more function and derivative information per iteration and hardly more storage or arithmetic per iteration than a standard method based on newton s method in extensive computational tests a tensor algorithm is significantly more efficient than a similar algorithm based on the standard linear model both on standard nonsingular test problems and on problems where the jacobian at the solution is singular

fingerprint pattern classification abstract this paper presents a new method for fingerprint classification in this method fingerprint images are divided into 32 32 subregions to obtain direction pattern next the relaxation smoothing process with singularity detection and convergency checking is performed starting from the singular regions found feature parameters of the fingerprint are obtained by extracting major flow line traces the result of the experiments shows that this approach is capable of classifying fingerprint patterns into more than ten categories

a levenberg marquardt algorithm with correction for singular system of nonlinear equations in this paper we propose a new lm algorithm for the singular system of nonlinear equations f x 0 where f x r n r n is continuously differentiable and f x is lipschitz continuous at every iteration not only a lm step but also a correction step are computed the lm parameter is taken as m email protected f email protected d where email protected 0 2 and m k is updated by the trust region technique under the local error bound condition which is weaker than nonsingularity we prove the convergence rate of the algorithm is min 2 email protected numerical results show that the new lm algorithm performs very well

approximation schemes for the linear quadratic optimal control problem associated with delay equations the linear regulator problem for delay equations is discussed we propose a theoretical solution involving riccati integral equations and then axiomatically discuss a general approximation scheme the details are given for spline and averaging approximations

convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems this paper studies the convergence and properties of the solutions of the riccati difference equation special emphasis is given to systems which are not necessarily stabilizable in the filtering sense particularly those having uncontrollable roots on the unit circle besides generalizing and unifying previous work the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

a new reduced order adaptive filter for state estimation in high dimensional systems a simple reduced order adaptive filter optimal in the sense of minimum prediction error is proposed for estimating the state of high dimensional systems in which the process and observation noise statistics are unknown it is shown that implementation of this adaptive filter requires the solution of only two linear difference equations the dimensions of which are the dimensions of the full and reduced states respectively and that no solution of either an algebraic riccati equation or a lyapunov equation is needed in addition substantial gain in computer memory and cpu time is obtained by parametrization of the filter gain in the form of the product of two matrices one of which is a prescribed projection from the reduced space onto the full space a twin experiment on data assimilation with a quasi geostrophic ocean model shows the efficiency of the proposed approach

singular point detection by shape analysis of directional fields in fingerprints this paper presents a new fingerprint singular point detection method that is type distinguishable and applicable to various fingerprint images regardless of their resolutions the proposed method detects singular points by analyzing the shapes of the local directional fields of a fingerprint image using the predefined rules all types of singular points upper core lower core and delta points can be extracted accurately and delineated in terms of the type of singular points in case of arch type fingerprints there exists no singular point but reference points for arch type fingerprints are required to be detected for registration therefore we propose a new reference point detection method for arch type fingerprints as well the result of the experiments on the two public databases fvc2000 2a fvc2002 2a with different resolutions demonstrates that the proposed method has high accuracy in locating each types of singular points and detecting the reference points of arch type fingerprints without regard to their image resolutions

discretisation of an infinite delay equation in this paper a banach phase space containing bc 0 and contained in c 0 is defined with which existence of a solution and convergence of a discrete scheme are proved for an infinite delay differential equation

on the convergence of the modified levenberg marquardt method with a nonmonotone second order armijo type line search recently fan j fan the modified levenberg marquardt method for nonlinear equations with cubic convergence math comput 81 2012 447 466 proposed a modified levenberg marquardt mlm method for nonlinear equations using a trust region technique global and cubic convergence of the mlm method is proved by fan 2012 12 under the local error bound condition which is weaker than nonsingularity the purpose of the paper is to investigate the convergence properties of the mlm method with a line search technique since the search direction of the mlm method may be not a descent direction standard line searches can not be used directly in this paper we propose a nonmonotone second order armijo line search which guarantees the global convergence of the mlm method moreover we prove that the unit step will be always accepted finally then cubic convergence of the mlm method is preserved under the local error bound condition some preliminary numerical results are also reported

pixel level singular point detection from multi scale gaussian filtered orientation field singular point as a global feature plays an important role in fingerprint recognition inconsistent detection of singular points apparently gives an affect to fingerprint alignment classification and verification accuracy this paper proposes a novel approach to pixel level singular point detection from the orientation field obtained by multi scale gaussian filters initially a robust pixel level orientation field is estimated by a multi scale averaging framework then candidate singular points in pixel level are extracted from the complex angular gradient plane derived directly from the pixel level orientation field the candidate singular points are finally validated via a cascade framework comprised of nested poincare indices and local feature based classification experimental results over the fvc 2000 db2 confirm that the proposed method achieves robust and accurate orientation field estimation and consistent pixel level singular point detection the experimental results exhibit a low computational cost with better performance thus the proposed method can be employed in real time fingerprint recognition

walking to singular points of fingerprints singular point is an essential global feature in fingerprint images existing methods for singular points detection generally visit each pixel or each small image block to determine the singular point that is to say existing methods require scanning the image to compute a quantity at each pixel or block and hence they are inevitably time consuming we propose a fast algorithm for detecting singular points by walking directly to them instead of scanning the image walking directional fields wdfs are established from the orientation field then following the walking directions on wdfs we can rapidly walk to the singular points the walking algorithm is extremely fast and easily implemented with acceptable accuracy further more its accuracy can also be improved by combining with state of the art methods we can rapidly walk to a candidate singular point then refine its location using existing more accurate method in the local area experimental results on datasets of spd2010 and fvc validate the high efficiency and satisfactory accuracy of the proposed algorithm highlightswe propose a novel fast method for singular point detection we can walk directly to singular points without scanning fingerprint images simplicity of the idea makes the algorithm easy to be implemented our algorithm can be combined with state of the art method to improve performance

a modified bfgs type quasi newton method with line search for symmetric nonlinear equations problems abstract in this paper using approximate gradient of the norm square metric function we present an inexact mbfgs method with line search for solving symmetric nonlinear equations which is a generalization of the mbfgs method proposed by li and fukushima 2001 for solving smooth unconstrained optimization the used approximate gradient of the proposed method only requires computing two residuals at every iteration and is easy to obtain by utilizing symmetric structure of the system we establish global convergence of the proposed method and report some numerical results

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

systematic methods for the computation of the directional fields and singular points of fingerprints the first subject of the paper is the estimation of a high resolution directional field of fingerprints traditional methods are discussed and a method based on principal component analysis is proposed the method not only computes the direction in any pixel location but its coherence as well it is proven that this method provides exactly the same results as the averaged square gradient method that is known from literature undoubtedly the existence of a completely different equivalent solution increases the insight into the problem s nature the second subject of the paper is singular point detection a very efficient algorithm is proposed that extracts singular points from the high resolution directional field the algorithm is based on the poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points furthermore a method is presented to estimate the orientation of the extracted singular points the accuracy of the methods is illustrated by experiments on a live scanned fingerprint database

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

three steps modified levenberg marquardt method with a new line search for systems of nonlinear equations three steps modified levenberg marquardt method for nonlinear equations was introduced by yang 2013 this method uses the addition of the levenberg marquardt lm step and two approximate lm steps as the trial step at every iteration using trust region technique the global and biquadratic convergence of the method is proved by yang the main aim of this paper is to introduce a new line search strategy while investigating the convergence properties of the method with this line search technique since the search direction of yang method may be not a descent direction standard line searches cannot be used directly in this paper we propose a new nonmonotone third order armijo type line search technique which guarantees the global convergence of this method while we use an adaptive lm parameter it is proved that the convergence order of the new method is biquadratic numerical results show the new algorithm is efficient and promising

prediction error sampling procedure based on dominant schur decomposition application to state estimation in high dimensional oceanic model abstract iterative procedure is described to generate patterns of dominant schur vectors of the system dynamics their roles in estimating the filter gain is study these patterns are produced by several integrations of the model from a set of perturbations this approach is motivated by a number of interesting results on stability of the filter whose gain is approximated in a subspace of dominant schur vectors a simple method for the filter design is presented which is aimed at overcoming the most serious drawback of advanced filtering algorithms for high dimensional systems related to very high computational cost in evaluation of the filter gain the resulting filter will be compared with the existing ones showing its relevance from a practical point of view in order to demonstrate its efficiency the new filter is tested on various experiments these experiments include the much studied problem of estimating the solution of the lorenz system as well as that of assimilating sea surface height observations in a high dimensional oceanic model it is shown that significant increases in efficiency can be obtained by using this filter and that the proposed filter is very promising for solving realistic assimilation problems in meteorology and oceanography

galerkin approximation of optimal linear filtering of infinite dimensional linear systems in this paper an implementable approximation of the infinite dimensional kalman filter is proposed for linear distributed systems corrupted by white noise it relies on a galerkin type treatment of both the riccati and the filter equations and it is shown to converge to the best linear estimate of the state for each sample path of the noise a basic tool is the study of the riccati equation on the hilbert space of hilbert schmidt operators on the state space numerical results are given for a case concerning delay differential equation

a note on the levenberg marquardt parameter abstract in c ma l jiang some research on levenberg marquardt method for the nonlinear equations appl math comput 184 2007 1032 1040 the lm parameter at the kth iteration is chosen as k f k 2 1 j k t f k 2 where f is the residual function j is the jacobi of f and 0 1 is a constant in this note we point out that the lm parameter can be any combination of f k 2 and j k t f k 2 provided it is positive furthermore we give a more general choice of the lm parameter and show that the lm method still preserves the quadratic convergence under the local error condition which is weaker than nonsingularity

a high order modified levenberg marquardt method for systems of nonlinear equations with fourth order convergence fan 2014 presented an accelerated modified levenberg marquardt method for nonlinear equations at every iteration the accelerated modified lm method computed not only a lm trial step but also an additional approximate lm step which employed a line search in this paper based on the accelerated modified lm method we compute the approximate lm step one more time at every iteration and obtain a high order accelerating modified levenberg marquardt method under the local error bound condition which is weaker than nonsingularity the convergence order of this new method is shown to be fourth a globally convergence is also given by the trust region technique numerical results show that the new method is efficient and could save many calculations of the jacobian

justification of input output methods for systems with unbounded control and observation the authors present definitions of feedback stabilizability and detectability that are weaker than those previously appearing in the literature stabilizability and detectability in this sense are sufficient to ensure an equivalence between internal and external stability for well posed systems furthermore stabilizability and detectability are shown to be preserved under feedback and other connections these results are linked to present a justification of input output controller design methods for systems with unbounded control and observation

structure theory and duality for time varying retarded functional differential equations on etudie les equations differentielles fonctionnelles a retard variant dans le temps dans le cadre de l espace etat c des fonctions continues et de l espace produit r n l p dans l espace c on considere deux concepts d etat l etat donne par la fonction initiale et l etat donne par le terme de forcage la theorie de dualite est basee sur ces 2 concepts on utilise explicitement deux operateurs structuraux f t et g t

a higher order levenberg marquardt method for nonlinear equations in this paper we present a high order levenberg marquardt method for nonlinear equations at every iteration not only a lm step is computed but also two approximate lm steps are computed which use the previous calculated jacobian under the local error bound condition which is weaker than nonsingularity the new method has biquadratic convergence a globally convergent lm algorithm is also given by the trust region technique numerical results show that the new fourth order lm algorithm performs very well and could save many jacobian calculations especially for large scale problems

on the stability properties of spline approximates for retarded systems this paper studies the qualitative properties of the spline approximation scheme for retarded functional differential equations introduced by kappel and salamon siam j control optim 25 1987 pp 1082 1117 it is shown that the approximating systems are stable for large n if the underlying retarded functional differential equation is stable in this case the approximating equations are in some sense uniformly with respect to the approximation index stable in the vector component of the state but not so in the complete state

spline approximation for systems of linear neutral delay differential equations abstract we derive a new finite dimensional semidiscrete approximation scheme for systems of linear neutral delay differential equations and prove convergence results our construction extends to neutral delay equations results which were previously only available for retarded delay equations

detection of singular points in fingerprint images abstract this paper describes a technique for the detection of singular points in a fingerprint image the singular points namely the core and the delta points are used as points of registration in fingerprint matching this method makes use of structural information culled from the directional histograms of the directional image of a fingerprint the usage of the histogram allows for a fairly high degree of noise tolerance

on the convergence of a modified regularized newton method for convex optimization with singular solutions in this paper we propose a modified regularized newton method for convex minimization problems whose hessian matrices may be singular the proposed method is proved to converge globally if the gradient and hessian of the objective function are lipschitz continuous under the local error bound condition we first show that the method converges quadratically which implies that x k x is equivalent to dist x k x where x is the solution set and x k x x then we in turn prove the cubic convergence of the proposed method under the same local error bound condition which is weaker than nonsingularity

fingerprint reference point detection for image retrieval based on symmetry and variation reference point plays an important role in fingerprint identification systems the reference point is widely used for the fingerprint retrieval in large scale databases this paper proposes a novel algorithm for detecting a convex core point as a unique reference point consistently and accurately for all types of fingerprints in order to detect robust core point candidates a modified complex filter called semi radial symmetry filter is proposed to detect correctly rotational symmetries of core points moreover a vertical orientation variation feature called voriv feature is proposed to remove spurious core points and concave core points therefore the proposed technique computes the variation and symmetry combined energy vscome then the reference point is located by searching the global vscome maximum the experimental results on the public database fvc2004 db1 set a show that the proposed technique exhibits a very high robustness and gets the best performance in comparing with other approaches in literature

an analysis of optimal modal regulation convergence and stability this paper treats the linear quadratic regulator problem for infinite dimensional second order in time linear oscillators we solve the problem approximately by modeling a finite number of mode

a twofold spline approximation for finite horizon lqg control of hereditary systems in this paper an approximation scheme is developed for the solution of the linear quadratic gaussian lqg control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay the solution here proposed is achieved by means of two approximating subspaces the first one to approximate the riccati equation for control and the second one to approximate the filtering equations since the approximating subspaces have finite dimension the resulting equations can be implemented the convergence of the approximated control law to the optimal one is proved simulation results are reported on a wind tunnel model showing the high performance of the method

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

an efficient two step trust region algorithm for exactly determined consistent systems of nonlinear equations abstract in this paper we propose a modified two step trust region algorithm for solving nonlinear systems two step trust region algorithms at every iteration use a trust region step and an approximate step by saving the jacobian matrix to have fewer computations we introduce a convex combination to modify the trust region subproblems along with an additional criterion to verify whether the first step is accepted or not we establish global and quadratic convergence of the algorithm under some mild assumptions numerical results show that the modified algorithm is efficient and promising

a modified two steps levenberg marquardt method for nonlinear equations the modified levenberg marquardt mlm method to solve nonlinear equations was introduced by fan 2012 this method uses an addition of the levenberg marquardt step and an approximate lm step as the trial step at every iteration using a trust region technique the global and cubic convergence of the mlm method under the local error bound condition is proved fan 2012 recently fan proposed an accelerated mlm algorithm by using a line search strategy to generate a modified lm step and showed that the convergence rate of the algorithm is min 1 2 3 which results the cubic convergence for 1 fan 2014 in this paper by introducing an adaptive lm parameter for amlm algorithm we propose an efficient amlm algorithm the cubic convergence of the new algorithm is presented while numerical experiments show the new algorithm is promising

an efficient algorithm for estimating noise covariances in distributed systems we present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems such systems arise typically by discretizing distributed parameter systems and their size renders computational efficiency a major consideration our adaptive filtering algorithm is based on the ideas of belanger and is algebraically equivalent to his algorithm the earlier algorithm however has computational complexity proportional to p6 where p is the number of observations of the system state while the new algorithm has complexity proportional to only p3 furthermore our formulation of noise covariance estimation as a secondary filter analogous to state estimation as a primary filter suggests several generalizations of the earlier algorithm the performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction

a corrected levenberg marquardt algorithm with a nonmonotone line search for the system of nonlinear equations in this paper we propose a corrected levenberg marquardt method for the system of nonlinear equations in which not only an l m step and a corrected step are computed at every iteration but also a nonmonotone line search to find a new iteration point will be performed if a trial step is not accepted to ensure the global convergence of the new method a new nonmonotone line search technique is introduced for the merit function the cubic convergence of the new method is proved under the local error bound condition which is weaker than nonsingularity some numerical results are reported which shows that the algorithm is quite effective

a new approach based on the newton s method to solve systems of nonlinear equations an alternative strategy for solving systems of nonlinear equations when the classical newton s method fails is presented the proposed strategy is an extension for systems based on the idea presented in the article ramos and vigo aguiar 2015 it relies in obtaining the approximate solutions of a given system of equations through solving an associated system obtained through the theory underlying the newton s method in this way the solutions of the associated system that are not 2 cycles of the newton iteration function provide solutions of the original system as it is usual in most cases the associated system cannot be solved exactly and some iterative procedure must be used for particular starting values solving the associated system with the newton s method results to be more efficient than the application of the newton s method to the original system some examples are given to illustrate the performance of the proposed strategy performance profiles are evaluated in terms of number of iterations error and cpu time

the optimal reduced order estimator for systems with singular measurement noise the optimal reduced order estimator is completely characterized by necessary conditions resulting from the optimal projection equations the solution consists of one riccati equation and two lyapunov equations coupled by two projections explicit expressions for all of the estimator parameters are given the relation between the reduced order singular estimator and the full order optimal singular estimator which is of reduced order itself is investigated it is shown that under certain conditions the optimal estimator is recovered from the reduced order estimator

on nonconvergence of adjoint semigroups for control systems with delays it is shown that the adjoints of a spline based approximation scheme for delay equations do not converge strongly

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

on the efficient low cost procedure for estimation of high dimensional prediction error covariance matrices abstract a simple efficient algorithm is proposed for estimating the prediction error covariance matrix which plays the key role for successful state estimation in very high dimensional systems the main results are obtained by introducing the hypothesis on the separability of vertical and horizontal structure of the error covariance matrix and its parameterization a new parameter optimization problem is formulated which is closely related to the nearest kronecker problem nkp this allows to estimate optimally the unknown parameters of the structured parametrized ecm as well as to approach numerically the solution of the traditional nkp in a simple and efficient way the algorithm for the state estimation will be detailed the results from experiments on parameter and state estimation problems for both moderate and high dimensional numerical models demonstrate a high effectiveness of the proposed filtering approach

a novel algorithm for detecting singular points from fingerprint images fingerprint analysis is typically based on the location and pattern of detected singular points in the images these singular points cores and deltas not only represent the characteristics of local ridge patterns but also determine the topological structure i e fingerprint type and largely influence the orientation field in this paper we propose a novel algorithm for singular points detection after an initial detection using the conventional poincare index method a so called doric feature is used to remove spurious singular points then the optimal combination of singular points is selected to minimize the difference between the original orientation field and the model based orientation field reconstructed using the singular points a core delta relation is used as a global constraint for the final selection of singular points experimental results show that our algorithm is accurate and robust giving better results than competing approaches the proposed detection algorithm can also be used for more general 2d oriented patterns such as fluid flow motion and so forth