discrete time techniques for time delay estimation basic aspects of time delay estimation tde based on sampled signals are investigated the direct cross correlation method is analyzed and compared to the average square difference function asdf and the addition only based average magnitude difference function amdf estimators their relative accuracy is theoretically evaluated and previous empirical results are explained it is shown that both the asdf and the amdf based estimators outperform the direct cross correlation based estimator for medium high signal to noise ratios moreover the amdf based estimator which avoids any multiplications significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the asdf based estimator

a fuzzy syllogistic reasoning schema for generalized quantifiers in this paper a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways i a number of different types of quantifiers logical absolute proportional comparative and exception taken from theory of generalized quantifiers and similarity quantifiers taken from statistics are considered and ii any number of premises can be taken into account within the reasoning process furthermore a systematic reasoning procedure to solve the syllogism is also proposed interpreting it as an equivalent mathematical optimization problem where the premises constitute the constraints of the searching space for the quantifier in the conclusion

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

comparison of three correlation coefficient estimators for gaussian stationary processes using independent samples from two stationary gaussian processes second order statistics are examined for the following three correlation estimators 1 the direct estimator 2 a hybrid sign estimator and 3 the polarity coincidence estimator in most cases increasing the number of samples by a factor of two or three allows one to use the simple polarity coincidence estimator with the same accuracy as the other two estimators

on approximate zeros and rootfinding algorithms for a complex polynomial on donne des criteres pour qu un nombre complexe soit une racine approchee d un polynome f par la methode de newton ou d euler d ordre k on construit des familles d algorithmes surement convergents

convergence of newton s method and inverse function theorem in banach space under the hypothesis that the derivative satisfies some kind of weak lipschitz condition a proper condition which makes newton s method converge and an exact estimate for the radius of the ball of the inverse function theorem are given in a banach space also the relevant results on premises of kantorovich and smale types are improved in this paper

improvement of a convergence condition for the durand kerner iteration abstract the durand kerner iteration is a well known simultaneous method for approximation of simple zeros of a polynomial by relating weierstrass correction and the minimal distance between approximations practical conditions for convergence have been obtained these conditions also ensure the existence of isolating discs for the polynomial roots i e each iteration step gives a refined set of inclusion discs in this paper refined conditions of convergence are given

point estimation of simultaneous methods for solving polynomial equations a survey ii the construction of computationally verifiable initial conditions which provide both the guaranteed and fast convergence of the numerical root finding algorithm is one of the most important problems in solving nonlinear equations smale s point estimation theory from 1981 was a great advance in this topic it treats convergence conditions and the domain of convergence in solving an equation f z 0 using only the information of f at the initial point z 0 the study of a general problem of the construction of initial conditions of practical interest providing guaranteed convergence is very difficult even in the case of algebraic polynomials in the light of smale s point estimation theory an efficient approach based on some results concerning localization of polynomial zeros and convergent sequences is applied in this paper to iterative methods for the simultaneous determination of simple zeros of polynomials we state new improved initial conditions which provide the guaranteed convergence of frequently used simultaneous methods for solving algebraic equations ehrlich aberth s method ehrlich aberth s method with newton s correction borsch supan s method with weierstrass correction and halley like or wang zheng method the introduced concept offers not only a clear insight into the convergence analysis of sequences generated by the considered methods but also explicitly gives their order of convergence the stated initial conditions are of significant practical importance since they are computationally verifiable they depend only on the coefficients of a given polynomial its degree n and initial approximations to polynomial zeros

efficient methods of estimate correlation functions of gaussian processes and their performance analysis new efficient methods to estimate crosscorrelation functions of gaussian signals are studied in these methods the covariance property of the gaussian distribution is utilized such that the correlation estimates can be computed with only additions to evaluate the performances of the methods exact expressions for the bias and variance of these estimators are formulated and utilized in comparing these methods with the conventional correlation estimator as a result we point out that these new methods can give estimates which are comparable to the conventional approach

a fast digital method of estimating the autocorrelation of a guassian stationary process given a zero mean stationary gaussian process x n it is shown that the autocorrelation can be estimated by hat r xx j c n sum min i 1 max n x i sign x i j where c n frac pi 2n 2 sum min i 1 max n x i this method is attractive since c n needs to he computed only once and sum min i 1 max n x i sign x i j can be computed by additions only moreover the shape of the autocorrelation given by hat r xx j c n can be computed by additions only

correlation estimators based on simple nonlinear transformations the computational cost of estimating correlations may be reduced by employing sums of simple nonlinear functions of the data a quadruplex transformation is presented and the performance of the associated estimator is analyzed for real and complex gaussian processes with independent observations the variance of the estimator is approximately 14 higher than that obtained by averaging lag products

a family of simultaneous zero finding methods abstract applying hansen patrick s formula for solving the single equation f z 0 to a suitable function appearing in the classical weierstrass method two one parameter families of interation functions for the simultaneous approximation of all simple and multiple zeros of a polynomial are derived it is shown that all the methods of these families have fourth order of convergence some computational aspects of the proposed methods and numerical examples are given

cumulant series expansion of hybrid nonlinear moments of et we will now present a simple example to illustrate the approach assume four receiver elements at 0 0 0 1 0 0 0 1 0 and 0 0 1 and a target at 2 0 0 by direct computation we find 6rl i 6r2 2 and 6ri 2 given that 6r i 6r2 6ri 2 h and that receivers are located at 0 0 0 i 0 0 0 i 0 and 0 0 i we will compute the coordinates of the target

on the new fourth order methods for the simultaneous approximation of polynomial zeros a new iterative method of the fourth order for the simultaneous determination of polynomial zeros is proposed this method is based on a suitable zero relation derived from the fourth order method for a single zero belonging to the schroder basic sequence one of the most important problems in solving polynomial equations the construction of initial conditions that enable both guaranteed and fast convergence is studied in detail for the proposed method these conditions are computationally verifiable since they depend only on initial approximations the polynomial coefficients and the polynomial degree which is of practical importance the construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed finally numerical examples and the comparison with existing fourth order methods are given

on a fast digital method of estimating the autocorrelation of a gaussian stationary process the zero mean stationary gaussian processes have the property that if they are input into an instantaneous nonlinear device the cross correlation of input and output is proportional to the auto correlation of the input this suggests an estimation procedure for the autocorrelation function based mainly on additions which is a modified type of the pcc polarity coincidence correlator the object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties as a reference some examples are provided which compare the behavior of the modified ppc estimator to the classical one based on products and additions

efficient autocorrelation estimation using relative magnitudes the relative magnitude estimator computes the normalized autocorrelation of a stationary gaussian process using simple nonlinear functions to eliminate most multiplications approximate expressions for bias and variance of the estimate are presented along with the results of a computer simulation the estimator performs well when compared to similar techniques

the guaranteed convergence of laguerre like method abstract the construction of initial conditions that provide a guaranteed convergence of zero finding methods has attracted a great deal of attention for many years in this paper we consider convergent properties of the laguerre like method of the fourth order for the simultaneous approximation of polynomial zeros using a procedure based on smale s point estimation theory and some recent results concerned with localization of complex polynomial zeros we state initial conditions which enable both the guaranteed and fast convergence of this method these conditions are computationally verifiable since they depend only on initial approximations polynomial coefficients and polynomial degree which is of practical importance

efficient polynomial root refiners a survey and new record efficiency estimates a typical iterative polynomial root finder begins with a relatively slow process of computing a crude but sufficiently close initial approximation to a root and then rapidly refines it the policy of using the same iterative process at both stages of computing an initial approximation and refining it however is neither necessary nor most effective the efficiency of an iteration at the former stage resists formal study and is usually decided empirically whereas formal study of the efficiency at the latter stage of refinement is not hard and is the subject of the current paper we define this local efficiency as log 1 0qd log 1 0 q 1 d q is the convergence order and d is the number of function evaluations per iteration it is inversely proportional to the number of flops involved assuming that about 2n flops are needed per evaluation of a polynomial of a degree n at a single point we extend the definition to cover the recent matrix methods for polynomial root finding as well as some methods that combine n approximations to all n roots to refine them simultaneously for the approximation of a single root of a polynomial of degree n the maximum local efficiency achieved so far is log 1 02 0 301 but we show its growth to infinity for simultaneous approximation of all n roots as n grows to infinity

approximate zeros of quadratically convergent algorithms smale s condition for a point to be an approximate zero of a func tion for newton s method is extended to the general quadratically convergent iterative algorithm it is shown in which way the bound in the condition is affected by the characteristics of the algorithm this puts the original condition of smale for newton s method in a more general perspective the results are also discussed in the light of numerical evidence

an efficient technique for high correlation estimation two sum based estimators are proposed as fast accurate methods for estimating the normalized acf of stationary processes for gaussian processes their performances are evaluated in terms of bias and covariance and are compared to the ones of the conventional direct estimator and of the hybrid sign and the polarity coincidence fast methods for high correlation values the proposed estimators exhibit the same accuracy as the direct estimator

computational complexity on the geometry of polynomials and a theory of cost ii this paper deals with traditional algorithms newton s method and a higher order generalization due to euler these iterations schemes and their modifications have had a great success in solving nonlinear systems of equations we give some understanding of this phenomenon by giving estimates of efficiency the problem we focus on is that of finding a zero of a complex polynomial

a note on the computational complexity of high correlation estimators two fast estimators of correlation coefficients namely the absolute difference average ada and the relative magnitude rm correlators have been proposed as well suited for high correlation estimation it is shown that equivalent implementations of the ada estimators actually require the same number of additions and comparisons as the rm estimator the computational costs of the two estimators are the same

a parallel algorithm for simple roots for polynomials abstract a method for finding simple roots of arbitrary polynomials based on divided differences is discussed theoretical background is presented for the case of simple roots numerical results are presented which show the algorithm finds simple and multiple zeros to an accuracy usually limited by the accuracy of polynomial evaluation the method is designed for a simd parallel computer the algorithm is compared to two other frequently used polynomial root finders the jenkins traub algorithm and laguerre s method

on iteration methods without derivatives for the simultaneous determination of polynomial zeros carstensen c and m s petkovic on iteration methods without derivatives for the simultaneous determination of polynomial zeros journal of computational and applied mathematics 45 1993 251 266 several algorithms for simultaneously approximating simple complex zeros of a polynomial are presented these algorithms use weierstrass corrections and do not require any polynomial derivatives it is shown that nourein s method is actually regula falsi for weierstrass corrections convergence analysis and computational efficiency are given for the considered methods in complex and circular arithmetic special attention is paid to hybrid methods that combine the efficiency of floating point arithmetic and the inclusion property of interval arithmetic

the theory of smale s point estimation and its applications abstract the main result of this paper is that we exact smale s point estimation theory i e without assuming k p z 1 p k z k k 2 being bounded by the point estimation convergence theorem of the ne method is set up by making use of the majorizing method the proof of the theorem is simple and precise while the required point estimation conditions are weaker than all those of known point estimation convergence theorems another result of this paper is an application of the above new theory to the durand kerner method we compare the point estimation conditions for the durand kerner method with other known point estimation conditions numerical results show that our results have evident advantages

an efficient higher order family of root finders a one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial based on a cubically convergent hansen patrick s family is studied we show that the convergence of the basic family of the fourth order can be increased to five and six using newton s and halley s corrections respectively since these corrections use the already calculated values the computational efficiency of the accelerated methods is significantly increased further acceleration is achieved by applying the gauss seidel approach single step mode one of the most important problems in solving nonlinear equations the construction of initial conditions which provide both the guaranteed and fast convergence is considered for the proposed accelerated family these conditions are computationally verifiable they depend only on the polynomial coefficients its degree and initial approximations which is of practical importance some modifications of the considered family providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions are also studied numerical examples demonstrate the convergence properties of the presented family of root finding methods

on the guaranteed convergence of the square root iteration method the construction of initial conditions which guarantee the convergence of the applied iterative method is one of the most important problems in solving nonlinear equations which attracted the great attention for many years in this paper we give a precise convergent analysis of the ostrowski like method of the fourth order for the simultaneous determination of polynomial zeros using a procedure based on smale s point estimation theory and some recent results related to the localization of complex polynomial zeros we state initial conditions which enable both the guaranteed and fast convergence of this method these conditions are computationally verifiable since they depend only on polynomial coefficients its degree and initial approximations which is of practical importance

a posteriori error bound methods for the inclusion of polynomial zeros using carstensen s results from 1991 we state a theorem concerning the localization of polynomial zeros and derive two a posteriori error bound methods with the convergence order 3 and 4 these methods possess useful property of inclusion methods to produce disks containing all simple zeros of a polynomial we establish computationally verifiable initial conditions that guarantee the convergence of these methods some computational aspects and the possibility of implementation on parallel computers are considered including two numerical examples a comparison of a posteriori error bound methods with the corresponding circular interval methods regarding the computational costs and sizes of produced inclusion disks were given

the convergence of a family of parallelzero finding methods abstract one of the crucial problems in solving polynomial equations is to state some kind of quantitative conditions that provide both safe and fast convergence in the spirit of smale s point estimation theory introduced in 1981 we construct in this paper computationally verifiable initial conditions which guarantee the convergence of the recently proposed one parameter family of methods of the fourth order for the simultaneous finding polynomial zeros these conditions are computationally verifiable since they depend only on initial approximations polynomial coefficients and polynomial degree which is of significant practical importance

a new fourth order family of simultaneous methods for finding polynomial zeros using a suitable fixed point relation with a complex parameter a new one parameter family of simultaneous methods of the fourth order for finding complex zeros of a polynomial is derived in ordinary complex arithmetic convergence analysis of the presented family is performed under computationally verifiable initial conditions which depend only on polynomial coefficients and initial approximations further improvements of the proposed family of methods are discussed and a modification for finding multiple zeros is presented some numerical results for various values of the parameter are given

point estimation of a family of simultaneous zero finding methods abstract the construction of initial conditions which provide the safe convergence of iterative processes is one of the most important problems in solving equations in this paper we give initial conditions for a one parameter family of iterative methods for the simultaneous determination of all simple zeros of a polynomial zeros this family has the order of convergence four and generates some new methods with good convergence properties the presented initial conditions are of practical importance since depend only of available data coefficients of a polynomial and initial approximations to the zeros

methods for estimating the autocorrelation function of complex gaussian stationary processes new methods for estimating the autocorrelation function acf of a complex gaussian stationary process are presented these methods are based on a general invariance property for the autocorrelation of a common class of the above processes this property suggests estimation procedures based on magnitude hard limiting and phase quantization the procedures are an extension of the relay estimator currently employed for real processes the computational cost and the general properties of the methods are discussed in particular some estimators especially suited for very simple implementations are considered the performance of the complex hybrid sign estimator is evaluated and compared to that of the classical direct estimator the proposed methods are attractive for many applications in the field of digital signal processing

performances of the hybrid sign correlation coefficient estimator for gaussian stationary processes the hybrid sign estimator is a method of estimating the autocorrelation coefficient for gaussian stationary processes based on sums in this correspondence the features of such an estimator are examined both for uncorrelated pairs of samples and for correlated pairs with an assigned autocorrelation function of the process a generalized estimator is considered by varying the spacing between the pairs of samples the performances in terms of bias covariance and variance are given in simple approximate formulas and compared in comprehensive diagrams to the direct estimator based on sums of products and the polarity coincidence estimator based on counters

on the convergence of wang zheng s method the choice of initial conditions ensuring safe convergence of the implemented iterative method is one of the most important problems in solving polynomial equations these conditions should depend only on the coefficients of a given polynomial p and initial approximations to the zeros of p in this paper we state initial conditions with the described properties for the wang zheng method for the simultaneous approximation of all zeros of p the safe convergence and the fourth order convergence of this method are proved