using triangular orthogonal functions for solving fredholm integral equations of the second kind the present work proposes a method for solving fredholm integral equations this is demonstrated by using a complementary pair of orthogonal triangular functions set derived from the well known block pulse functions set the operational matrices for integration product of two triangular functions and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of fredholm integral equation to the solution of algebraic equations illustrative examples are included to show the high accuracy of the estimation and to demonstrate validity and applicability of the method

optimization of quiescent response in partially adaptive beamformers the adaptive weights utilize only a fraction of the available degrees of freedom in partially adaptive lcmv linearly constrained minimum invariance beamformers two procedures are presented for incorporating unused degrees of freedom into the beamformer s quiescent response in one case the quiescent response is chosen to approximate a desired quiescent response and in the other case it is chosen to maximize the average interference cancellation over a set of likely interference scenarios a sidelobe canceling interpretation indicates that maximization of average interference cancellation results in quiescent weights that optimize the sum of the white noise gain and the error between the quiescent response and the class of responses which the adaptive branch can synthesize simulations illustrate the utility of the methods

on the index for array optimization and the discrete prolate spheroidal functions a class of array optimization problems is considered in which we seek to optimize the array response in a specified angular sector the optimization of array directivity is shown to be a special limiting case of these problems as the width of the specified angular sector approaches zero the optimum array patterns are also shown to be related to the well known prolate spheroidal functions

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

wide band nulling performance versus number of pattern constraints for an array antenna the problem of wide band pattern hulling for an array antenna is addressed in particular the relation between the number of constraints imposed and the sidelobe suppression achieved the two constraint methods considered are multiple nulling over a narrow angular sector and hulling of the pattern and its derivatives at a single point to first order the sidelobe cancellation is shown to be independent of the actual pattern type and is determined by only two parameters the number of null constraints m and the number of sidelobes v to be cancelled the latter parameter directly translates into a desired hulling bandwidth delta f a numerical solution to the problem is offered in the form of curves from which the number of nulls required to suppress a jammer over a given bandwidth can be conveniently estimated this number is indicative of how many degrees of freedom a conventional adaptive antenna system must allocate to attain a specific hulling performance

dynamics of a family of chebyshev halley type methods in this paper the dynamics of the chebyshev halley family is studied on quadratic polynomials a singular set that we call cat set appears in the parameter space associated to the family this set has interesting similarities with the mandelbrot set the parameter space has allowed us to find different elements of the family which have bad convergence properties since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method

attracting cycles for the relaxed newton s method we study the relaxed newton s method applied to polynomials in particular we give a technique such that for any n 2 we may construct a polynomial so that when the method is applied to a polynomial the resulting rational function has an attracting cycle of period n we show that when we use the method to extract radicals the set consisting of the points at which the method fails to converge to the roots of the polynomial p z z m c this set includes the julia set has zero lebesgue measure consequently iterate sequences under the relaxed newton s method converge to the roots of the preceding polynomial with probability one

spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

large modular structures for adaptive beamforming and the gram schmidt preprocessor an alternate derivation of the modular structure for linearly constrained minimum variance beamforming proposed in liu and van veen 1991 is presented using a vector space approach this approach eliminates the tedious algebra employed in that paper and establishes the relationship between the modular structure and the gram schmidt preprocessor mozingo and miller 1980 the modular structure is obtained using a factorization of the orthogonal projection operator in hilbert space the gram schmidt preprocessor is a special case of the general modular decomposition it is also shown that these structures offer computational efficiencies when multiple beamformers are implemented simultaneously

multiple window based minimum variance spectrum estimation for multidimensional random fields spectrum analysis is viewed as the problem of estimating the power of a process contained within narrow bands this view leads naturally to consideration of filter based methods for estimating spectra multiple window based estimators where the power in a band is estimated as the average of the powers estimated at the outputs of multiple filters are considered the filters are designed using a linearly constrained minimum variance criterion commonly employed in adaptive beamforming this results in filters that automatically adjust their sidelobes to minimize leakage of energy from outside the band of interest expressions for the bias and variance of the power estimates are derived assuming the sample covariance matrix estimate is used to estimate the data covariance matrix and that the data are independent and identically gaussian distributed these expressions lead to the definition of a performance factor that indicates the degree of variance reduction obtained via multiple window processing a technique for obtaining increased suppression of energy leaking through the filter sidelobes at the expense of the response fidelity to energy in the band is presented simulations are presented to illustrate the effectiveness of the technique

a new set of linear constraints for broad band time domain element space processors a new set of linear constraints for designing broad band time domain element space antenna array processors is presented the set of linear constraints is used to ensure that a desired look direction response of the processor over a frequency band of interest can be closely approximated the design technique is posed in such a way that three types of presteering can be handled no presteering coarse presteering and exact presteering the elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors the relationship that the new processor has to other broad band processors is also established furthermore the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation

the cramer rao lower bound for directions of arrival of gaussian cyclostationary signals the cramer rao lower bound on the variance of estimates of directions of arrival signal strengths and carrier frequencies and phases of cyclostationary signals arriving at an array is considered numerical evaluations of the bound for the estimates of directions of arrival show that it can be orders of magnitude lower than the corresponding bound for stationary signals despite the great number of unknown parameters in the former case comparisons with the mean squared error of direction estimates obtained by the cyclic least squares algorithm show that the bound is not overly optimistic

families of rational maps and iterative root finding algorithms in this paper we develop a rigidity theorem for algebraic families of rational maps and apply it to the study of iterative root finding algorithms we answer a question of smale s by showing there is no generally convergent algorithm for finding the roots of a polynomial of degree 4 or more we settle the case of degree 3 by exhibiting a generally convergent algorithm for cubics and we give a classification of all such algorithms in the context of conformal dynamics our main result is the following a stable algebraic family of rational maps is either trivial all its members are conjugate by mobius transformations or affine its members are obtained as quotients of iterated addition on a family of complex tori our classification of generally convergent algorithms follows easily from this result as another consequence of rigidity we observe that the eigenvalues of a nonaffine rational map at its periodic points determine the map up to finitely many choices this implies that bounded analytic functions nearly separate points on the moduli space of a rational map

numerical solution of multi order fractional differential equations using generalized triangular function operational matrices present article proposes numerical technique for the solution of linear and nonlinear multi order fractional differential equations the proposed method is based on newly computed generalized triangular function operational matrices for riemann liouville fractional order integral theoretical error analysis is performed to estimate the upper bound of absolute error between the exact riemann liouville fractional order integral and its approximation in the triangular functions domain most fractional differential equations do not have closed form solutions development of effective numerical techniques has been an interesting research topic for decades in this context this paper proposes a numerical technique for solving linear and nonlinear multi order fractional differential equations based on newly computed generalized triangular function operational matrices for riemann liouville fractional order integral the orthogonal triangular functions are evolved from a simple dissection of piecewise constant orthogonal block pulse functions theoretical error analysis is performed to estimate the upper bound of absolute error between the exact riemann liouville fractional order integral and its approximation in the triangular functions domain numerical examples are considered for investigating the applicability and effectiveness of proposed technique to solve multi order fractional differential equations the results encourage the use of orthogonal tfs for analysis of real processes exhibiting fractional dynamics

study of iterative methods through the cayley quadratic test many iterative methods for solving nonlinear equations have been developed recently the main advantage claimed by their authors is the improvement of the order of convergence in this work we compare their dynamical behavior on quadratic polynomials with the one of newton s scheme this comparison is defined in what we call cayley quadratic test cqt which can be used as a first test to check the efficiency of such methods moreover we make a brief insight in cubic polynomials

a construction of attracting periodic orbits for some classical third order iterative methods we use a family of root finding iterative methods for finding roots of nonlinear equations we present a procedure for constructing polynomials so that superattracting periodic orbits of any prescribed period occur when these methods are applied this family includes chebyshev s method halley s method the super halley method and the c methods as particular cases

basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations several optimal eighth order methods to obtain simple roots are analyzed the methods are based on two step fourth order optimal methods and a third step of modified newton the modification is performed by taking an interpolating polynomial to replace either f z n or f z n in six of the eight methods we have used a hermite interpolating polynomial the other two schemes use inverse interpolation we discovered that the eighth order methods based on jarratt s optimal fourth order methods perform well and those based on king s or kung traub s methods do not in all cases tested the replacement of f z by hermite interpolation is better than the replacement of the derivative f z

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

an iterative algorithm for the computation of the mvdr filter statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter or constraint vector and generates a sequence of filters that converges to the minimum variance distortionless response mvdr solution for any positive definite input autocorrelation matrix computationally the algorithm is a simple noninvasive recursive procedure that avoids any form of explicit autocorrelation matrix inversion decomposition or diagonalization theoretical analysis reveals basic properties of the algorithm and establishes formal convergence when the input autocorrelation matrix is replaced by a conventional sample average positive definite estimate the algorithm effectively generates a sequence of mvdr filter estimators the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion smi estimator in fact formal convergence of the estimator sequence to the smi estimate is established however for short data records it is the early nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean square estimation error constraint lms rls type orthogonal multistage decomposition as well as plain and diagonally loaded smi estimates an illustrative interference suppression example is followed throughout this presentation

complex dynamics of derivative free methods for nonlinear equations the dynamical behavior of two iterative derivative free schemes steffensen and m4 methods is studied in case of quadratic and cubic polynomials the parameter plane is analyzed for both procedures on quadratic polynomials different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients the property of immersion of the basins of attraction in all cases is analyzed

ball convergence comparison between three iterative methods in banach space under hypothese only on the first derivative we present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a banach space setting the convergence ball and error estimates are given for these methods under hypotheses only on the first frechet derivative in contrast to earlier studies such as adomian 1994 1 babajee et al 2008 13 cordero and torregrosa 2007 17 cordero et al 18 darvishi and barati 2007 19 using hypotheses reaching up to the fourth frechet derivative although only the first derivative appears in these methods this way we expand the applicability of these methods numerical examples are also presented in this study

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

an efficient optimal family of sixteenth order methods for nonlinear models abstract the principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ newton s method to further develop new interesting optimal scheme of order sixteen this scheme requires four evaluations of the involved function and one evaluation of its first order derivative at each step so it is being optimally consistent with the conjecture of kung traub in addition theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence moreover the conjugacy maps and the strange fixed points of some iterative methods are discussed their basins of attractions are also given to show their dynamical behavior around the simple roots from the numerical experiments we find that our methods perform better than the existing ones when we checked the performance on a concrete variety of nonlinear equations

solution of time varying delay systems using an adaptive collocation method abstract an adaptive legendre gauss radau collocation method is presented for solving time varying delay systems by dividing the domain of the problem into a uniform mesh the delay system is replaced with a sequence of initial value problems the method developed in this paper adjusts both the mesh spacing and the degree of the polynomial on each mesh interval in order a specified error tolerance is satisfied we investigate some error estimates on the whole domain of interest some numerical examples are given and comparisons with other methods are made to demonstrate the efficiency and accuracy of the proposed method

numerical solution of nonlinear volterra fredholm integro differential equations via direct method using triangular functions an effective direct method to determine the numerical solution of the specific nonlinear volterra fredholm integro differential equations is proposed the method is based on new vector forms for representation of triangular functions and its operational matrix this approach needs no integration so all calculations can be easily implemented some numerical examples are provided to illustrate the accuracy and computational efficiency of the method

a family of higher order iterations free from second derivative for nonlinear equations in r abstract the aim of this article is to develop a family of higher order iterations free from second derivative for solving nonlinear equations in r their theoretical computational and dynamical aspects are fully investigated and theorems are established to provide their order of convergence and asymptotic error constant it is observed that the family includes sixth order methods and for a particular case its eighth order can be achieved in this family methods use three functions and one first derivative evaluations the family of methods can be shown to be optimal by using kung traub conjecture a number of numerical examples are worked out to demonstrate the applicability of these methods the improved results are obtained in comparison to some of the existing robust methods on the considered test examples local convergence analysis and dynamical study of the proposed family of methods are also carried out

dynamics of a new family of iterative processes for quadratic polynomials in this work we show the presence of the well known catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations in fact we introduce a family of methods depending on a parameter m n 0 these methods reach the order of convergence m 2 when they are applied to quadratic polynomials with different roots newton s and chebyshev s methods appear as particular choices of the family appear for m 0 and m 1 respectively we make both analytical and graphical studies of these methods which give rise to rational functions defined in the extended complex plane firstly we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the catalan numbers secondly we make an incursion into its dynamical behavior in fact we show that the rational maps related to these methods can be written in terms of the entries of the catalan triangle next we analyze its general convergence by including some computer plots showing the intricate structure of the universal julia sets associated with the methods

on the eigenstructure of the signal only tempo spatial covariance matrix of broad band sources using a circular array the eigenstructure of the signal only part of the data covariance matrix for broadband sources is considered it is well known that unlike the narrowband case all eigenstructure parameters the matrix rank eigenvalues and eigenvectors depend on source spectral and spatial parameters as well as on the relationship between sources it is proved that when a two dimensional equally spaced circular array with flat spectrum broadband sources is used the eigenstructure of the signal only tempo spatial covariance matrix tscm has properties similar to those for the narrowband case most importantly the effective rank of the tscm depends only on the number of sources consequently the authors suggest an alternative approach for resolving frequency location ambiguity in the broadband case that may lead to an effective eigenstructure based parameter estimation algorithm of the music type

using direct method for solving variational problems via triangular orthogonal functions this paper establishes a ritz direct method for solving variational problems via a set of complementary pair of triangular orthogonal functions derived from well known block pulse functions the properties of triangular functions are presented and the operational matrices for integration product and some formulas for calculating definite integration of product are derived and utilized to obtain a clear procedure to reduce a variational problem to the solution of algebraic equations illustrative examples are included to show the high accuracy of the estimation and to demonstrate validity and applicability of the method

analysis parameter estimation and optimal control of time delay systems via chebyshev series the chebyshev delay operational matrix is introduced first and then applied to approximate the solutions of linear time invariant and time varying delay systems with arbitrary time delay the parameter identification problem of the delay control system is also studied furthermore an approximate solution of the optimal control problem with quadratic performance measure is then discussed four examples are given and the results are shown to be very accurate and satisfactory

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

broadband doa estimation using spatial only modeling of array data most of the existing techniques for doa estimation of broadband sources use both spatial and temporal modeling this may lead to increased complexity besides a large algorithmic delay we propose a technique that employs only spatial information in the form of a single spatial array covariance matrix assuming the source to have an ideal bandpass power spectral density we formulate two subspace based search functions for the estimation of the doas of broadband sources one of these employs a multidimensional search in the parameter space whereas the other requires a music like one dimensional 1 d search the multidimensional cost function is shown to be consistent yields performance close to the cramer rao cr bound and is insensitive to correlation between sources both the proposed methods are shown to be robust to deviations from the assumption of ideal bandpass power spectral density used in their formulation

basin attractors for various methods for multiple roots abstract there are several methods for approximating the multiple zeros of a nonlinear function when the multiplicity is known the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss all known methods of orders two to four and present the basin of attraction for several examples

stability study of eighth order iterative methods for solving nonlinear equations in this paper we study the stability of the rational function associated to a known family of eighth order iterative schemes on quadratic polynomials the asymptotic behavior of the fixed points corresponding to the rational function is analyzed and the parameter space is shown in which we find choices of the parameter for which there exists convergence to cycles or even chaotical behavior showing the complexity of the family moreover some elements of the family with good stability properties are obtained

a modular structure for implementation of linearly constrained minimum variance beamformers a description is given of a cascade decomposition of the generalized sidelobe canceller gsc implementation for linearly constrained minimum variance beamformers the gsc is initially separated into an adaptive interference cancellation module followed by a nonadaptive beamformer the authors prove that the adaptive interference cancellation module can be decomposed into a cascade of first or higher order adaptive interference cancellation modules where the order corresponds to the number of adaptive degrees of freedom represented in the module this distributes the computational burden associated with determining the adaptive weights over several lower order problems and facilitates simultaneous implementation of beamformers with differing numbers of adaptive degrees of freedom

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

generalized eigenspace based beamformers the generalized eigenspace based beamformer geib is presented here which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer lcmvb the weight vector of the geib is found by projecting the lcmvb weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix the geib and the lcmvb have the same responses to the desired signal and the interferers however the weight vector of the geib has a smaller norm and generates a lower output noise power an additional advantage of the geib is that the linear constraints can be treated flexibly i e each linear constraint can be chosen to be preserved or not preserved the cost of preserving a linear constraint is to get more output noise power in addition to developing the geib we discuss the effects of imposing linear constraints on the output noise powers of the geib and the lcmvb computer simulations are also presented that demonstrate the merits of the geib

eigenstructure based partially adaptive array design a procedure is presented for designing partially adaptive arrays having nearly fully adaptive performance under steady state conditions theory predicts that the required adaptive dimension is less than or equal to the rank of the spatially temporally correlated portion of the interference correlation matrix for arbitrary linearly constrained minimum variance beamformers knowledge of the eigenstructure of the interference correlation matrix is required to implement a beamformer with this adaptive dimension to avoid adaptive estimation of the eigenstructure the eigenstructure of an averaged correlation matrix which spans the interference scenarios of interest is utilized and the adaptive dimension is given by the rank of the averaged correlation matrix construction of a transformation for reducing adaptive dimension is addressed simulations illustrating the utility of the eigenstructure approach are provided

analysis of time varying delay systems via triangular functions abstract this paper presents a method for finding the analysis of time varying delay systems using triangular functions we present the properties of the triangular functions the operational matrices of integration delay and product are utilized to reduce the solution of delay systems to the solution of algebraic equations illustrative examples is included to demonstrate the validity and applicability of the technique

basin attractors for various methods abstract there are many methods for the solution of a nonlinear algebraic equation the methods are classified by the order informational efficiency and efficiency index here we consider other criteria namely the basin of attraction of the method and its dependence on the order we discuss several methods of various orders and present the basin of attraction for several examples it can be seen that not all higher order methods were created equal newton s halley s murakami s and neta johnson s methods are consistently better than the others in two of the examples neta s 16th order scheme was also as good

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

some higher order iteration functions for solving nonlinear models abstract in this paper we present a new efficient sixth order family of jarratt type methods for solving scalar equations then we extend this family to the multidimensional case preserving the same order of convergence we also discuss the theoretical convergence properties of the proposed scheme in the case of scalar as well as multidimensional case the derivation of these schemes are based on weight function approach and free disposable parameters we also demonstrate the applicability of them on total six number of problems first five are real life problems namely continuous stirred tank reactor cstr chemical engineering the trajectory of an electron in the air gap between two parallel plates hammerstein integration and boundary value problems last one is the standard academic test problem in addition numerical comparisons are made to show the performance of the proposed iterative techniques with the existing techniques of the same order in the scalar as well as multi dimensional case finally on the basis of numerical results we conclude that our techniques perform better in terms of residual error error between the two consecutive iterations asymptotic error constant term and approximated root as compared to the existing ones of same order in scalar as well as multidimensional case

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

on optimal fourth order iterative methods free from second derivative and their dynamics in this paper new fourth order optimal root finding methods for solving nonlinear equations are proposed the classical jarratt s family of fourth order methods are obtained as special cases we then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three the basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance