solution of a system of nonlinear equations by adomian decomposition method in this paper the adomian decomposition method is applied to solve a system of nonlinear equations convergence of the method is proved and some examples are presented to illustrate the method

super cubic iterative methods to solve systems of nonlinear equations two super cubic convergence methods to solve systems of nonlinear equations are presented the first method is based on the adomian decomposition method we state and prove a theorem which shows the cubic convergence for this method but numerical examples show super cubic convergence the second method is based on a quadrature formulae to obtain the inverse of jacobian matrix numerical examples show high order convergence for both methods

performance analysis of the optimum beamformer in the presence of correlated sources and its behavior under spatial smoothing in this paper we first study the signal cancellation and interference rejection effects of the optimum constrained least squares or minimum variance beamformer in the presence of partially and fully correlated interfering sources in particular we derive expressions for the output power and the gain in the interference direction of the beamformer in terms of the source powers correlation and the sensor noise power and show quantitatively the penalties arising from increasing correlation in several scenarios of interest next we show that spatial smoothing progressively decorrelates the sources at a rate that depends on the spacing and directions of the sources and thus relate the degree of smoothing to the improvement in signal cancellation and interference rejection behavior provided by spatial smoothing results of computer simulations are included to support our analysis

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

a note on the local convergence of iterative methods based on adomian decomposition method and 3 node quadrature rule abstract darvishi and barati m t darvishi a barati super cubic iterative methods to solve systems of nonlinear equations appl math comput 2006 10 1016 j amc 2006 11 022 derived a super cubic method from the adomian decomposition method to solve systems of nonlinear equations the authors showed that the method is third order convergent using classical taylor expansion but the numerical experiments conducted by them showed that the method exhibits super cubic convergence in the present work using ostrowski s technique based on point of attraction we show that their method is in fact fourth order convergent we also prove the local convergence of another fourth order method from 3 node quadrature rule using point of attraction

extended newton s method for a system of nonlinear equations by modified adomian decomposition method abstract in this paper we present some efficient numerical algorithms for solving a system of two nonlinear equations with two variables based on newton s method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

fast algorithms for l p deconvolution this paper discusses two algorithms for l p 1 leq p leq 2 deconvolution one iterative reweighted least squares irls is discussed with an eye toward improving its computational efficiency while the other residual steepest descent rsd is considered in an attempt to improve its convergence properties in the first case fast fourier transforms are used to reduce the number of computations in the second a new rescaling procedure which enhances rsd convergence is introduced the lack of stability of l 1 filters and its implications are discussed simple examples are used to illustrate pertinent concepts

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

floquet solutions for the 1 dimensional quasi periodic schrodinger equation we show that the 1 dimensional schrodinger equation with a quasiperiodic potential which is analytic on its hull admits a floquet representation for almost every energye in the upper part of the spectrum we prove that the upper part of the spectrum is purely absolutely continuous and that for a generic potential it is a cantor set we also show that for a small potential these results extend to the whole spectrum

the schrodinger equation with a quasi periodic potential we consider the schrodinger equation dx2 v e cosx cos cix 0 v eqi where e is small and a satisfies the diophantine inequality lp qcl c q2 forp qez q 0 we look for solutions of the form ikx ikx in x im ax 0 m x e q x e 2m ne inxne e if we try to solve for v v mn we are led to the schrodinger equation on the lattice z2 h k q ba v k q en where a is the discrete laplacian without diagonal terms and v k is some 2 potential on z we have two main results 4 for e sufficiently small h k has pure point spectrum for almost every k 2 for e sufficiently small the operator d dx 2 e cosx cos ax has no point spectrum to prove our results we must get decay estimates on the green s function e h 1 the decay of the eigenfunction follows from this in general we must keep track of small divisors which can make the green s function large this is accomplished by a kam kolmogorov arnold moser type of multiscale perturbation analysis

linear prediction of speech with a least absolute error criterion most methods for linear prediction of speech are based on a least square error criterion l 2 criterion in this paper it is shown that the robustness of a least absolute error criterion l 1 criterion is particularly well adapted to the analysis of voiced sounds the well known linear programming l 1 algorithms have two important drawbacks the stability of the synthesis filter is not guaranteed and the computation load is too heavy for real time analysis all these problems are alleviated by the new l 1 algorithm proposed in this paper experiments show comparable efficiency with classical l 2 methods

on the properties of reduced order kalman filters several known results are unified by considering properties of reduced order kalman filters for the case in which the number of noise sources equals the number of observations it is shown that the reduced order kalman filter achieves zero steady state variance of the estimation error if and only if the plant has no transmission zeros in the right half plane since these would be among the poles of the kalman filter the reduced order kalman filter cannot achieve zero variance of the estimation error if the number of independent noise sources exceeds the number of observations it is also shown that the reduced order kalman filter achieves the generalized doyle stein condition for robustness when the noise sources are colocated with the control inputs when there are more observations than noise sources additional noise sources can be postulated to improve the observer frequency response without diminishing robustness

linearized reduced order filtering a reduced order version of extended kalman filtering is presented in which both the filtering equation and the associated riccati equation have been reduced in dimension to allow for real time processing the procedure for designing the reduced order filter is similar to that for designing the extended kalman filter the same approximations being applied one technique useful for limiting the computational burden in a linearized filter design problems is presented and illustrated by an example the primary limitation of the result is that the nonlinearity must be in terms of the vector to be estimated

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

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

functional magnetic resonance inverse imaging of human visuomotor systems using eigenspace linearly constrained minimum amplitude elcma beamformer recently proposed dynamic magnetic resonance mr inverse imaging ini is a novel parallel imaging reconstruction technique capable of improving the temporal resolution of blood oxygen level dependent bold contrast functional mri fmri to the order of milliseconds at the cost of moderate spatial resolution volumetric ini reconstructs spatial information from projection data by solving ill posed inverse problems using simultaneous acquisitions from a rf coil array previously a spatial filtering technique based on linearly constrained minimum variance lcmv beamformer was suggested to localize the hemodynamic changes of dynamic ini data with improved spatial resolution and sensitivity here we report an advancement of the spatial filtering method which combines the eigenspace projection of the measured data and the l1 norm minimization of the spatial filters output noise amplitude to further improve the detection power of bold contrast fmri data using numerical simulation and in vivo data we demonstrate that this eigenspace linearly constrained minimum amplitude elcma beamformer can reconstruct spatiotemporal hemodynamic signals with high statistical significance values and high spatial resolution in event related two choice reaction time visuomotor experiments

a fourth order method from quadrature formulae to solve systems of nonlinear equations in this paper we obtain a fourth order convergence method to solve systems of nonlinear equations this method is based on a quadrature formulae a general error analysis providing the fourth order of convergence is given numerical examples show the fourth order convergence this method does not use the second order frechet derivative

operators with singular continuous spectrum iii almost periodic schrodinger operators we prove that one dimensional schrodinger operators with even almost periodic potential have no point spectrum for a dense g in the hull this implies purely singular continuous spectrum for the almost mathieu equation for coupling larger than 2 and a dense g in even if the frequency is an irrational with good diophantine properties

on essential spectra of singular linear hamiltonian systems abstract the paper is concerned with essential spectra of singular linear hamiltonian systems of arbitrary order with arbitrary equal defect indices several sufficient conditions for the essential spectral points are given in terms of the number of linearly independent square integrable solutions of the corresponding hamiltonian system and a sufficient and necessary condition for the essential spectral points is obtained for hamiltonian systems of even order with one singular endpoint an advantage of these results is that one can determine the essential spectral points of hamiltonian systems by the information of solutions obtained by numerous tools available in the fundamental theory of differential equations in addition two illustrative examples are provided to show how to get some information about the essential spectrum by our results

l sub 2 and l sub 1 beamformers recursive implementation and performance analysis studies array beamformers as optimal waveform estimators the authors apply an inverse problem formulation presenting an integrated design to quadratic l sub 2 and least absolute value l sub 1 beamformers the general solution of the l sub 2 beamformers is parameterized by a regularizing parameter that weights the confidence placed by the designer on prior knowledge versus the quality of the measurements this regularizing parameter is used to establish an equivalence between alternative l sub 2 beamformers the authors then develop time recursive implementations of the l sub 2 and l sub 1 beamformers the performance of these beamformers is studied next the authors show that 1 in the presence of correlated arrivals the mmse beamformer uses constructively the correlation between incoming signals in reconstructing the estimated field while rejecting the uncorrelated returns and 2 the l sub 1 beamformer has the ability to adjust itself to unexpected noise conditions because it is considerably more robust than the l sub 2 beamformers to unmodeled impulsive noise or to the occurrence of malfunctioning sensors the analysis is confirmed by simulated studies

an effective iterative method for computing real and complex roots of systems of nonlinear equations a simple and flexible iterative method is proposed to determine the real or complex roots of any system of nonlinear equations f x 0 the idea is based on passing defined functions g j x j j 1 n tangent to f i x j i j 1 n at an arbitrary starting point choosing g j x j in the form of x j k j or k j x j or any other reversible function compatible to f i x j where k is obtained for the best correlation with the function f i x j gives an added freedom which in contrast with all existing methods accelerates the convergence the method that was first proposed for computing the roots of any single function is now adopted for a system of nonlinear equations this method is compared to some classical and famous methods such as newton s method and newton simpson s method the results show the effectiveness and robustness of this new method

predictability and unpredictability in kalman filtering the authors study the dynamical behavior of the kalman filter when the given parameters are allowed to vary in a way which does not necessarily correspond to an underlying stochastic system this may correspond to situations in which the basic parameters are chosen incorrectly through estimates the authors show that as has been suggested by kalman the filter equations converge to a limit corresponding to a steady state filter for a subset of the parameter space which is much larger than that corresponding to bona fide stochastic systems more surprisingly in the complement of this subset the filtering equations behave in both a regular and an unpredictable manner representative of some of the basic aspects of chaotic dynamics this interesting dynamical behavior occurs already for one dimensional filters and a complete phase portrait in this case is given

some iterative methods for solving a system of nonlinear equations in this paper we suggest and analyze two new two step iterative methods for solving the system of nonlinear equations using quadrature formulas we prove that these new methods have cubic convergence several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods these new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations

on the spectrum of odd order self adjoint ordinary differential operators on the real line with quasi periodic coefficients in this paper we prove that an odd order self adjoint differential operator on the real line with quasi periodic coefficients has only absolute continuous simple spectrum for large enough energies ordinary differential operators with quasi periodic coefficients have been studied a lot during the last 20 years these operators arise naturally from physical considerations people have mainly been interested in the one dimensional schro dinger operator with a quasi periodic potential see be te din sin eli ji si mo mo po su and so sp such hamiltonians come up naturally in solid state physics see pa fi in this paper we study ordinary differential operators of higher order with quasi periodic coefficients such operators also come up in physics for example in the study of boussinesq s equation article no de963225