Power Sums Of Roots Research Articles

On calculating partial sums of multiple numerical series by methods of Computer Algebra

A method to calculate partial sums of some multiple numerical series arising when searching for the resultant of a polynomial and an entire function is proposed. One can apply a symbolic algorithm that uses recurrent Newton formulas to find power sums of roots included in this formula without finding the very roots of the system. The algorithm that implements the proposed approach to calculate partial sums of multiple numerical series is implemented in Maple. Examples of using this algorithm to find partial sums of some classes of multiple numerical series are given.

On computing residue integrals for a class of nonlinear transcendental systems

A method of computing residue integrals with integration over certain cycles for systems of transcendental equations is presented. Such integrals are connected to the power sums of roots for a certain system of equations. The described approach can be used for developing methods for the elimination of unknowns from transcendental systems.

Root power sums and Chebyshev polynomials

We determine sequences of polynomials with rational coefficients that have certain postulated values for their root power sums. These, in turn, determine four families of orthogonal polynomials that can be expressed in terms of Chebyshev polynomials by a change of variables. We examine properties of these sequences of polynomials, two of which have already been studied in a previous paper.

On finding residue integrals for a class of systems of non-algebraic equations

A method of finding residue integrals for systems of non-algebraic equations containing analytic functions is presented. Such integrals are connected to the power sums of roots for a certain system of equations. The described approach can be used for developing methods for the elimination of unknowns from systems of non-algebraic equations.

Polynomial Long Division and Root Power Sums

(2014). Polynomial Long Division and Root Power Sums. Math Horizons: Vol. 21, No. 3, pp. 20-23.

Finding residue integrals for systems of non-algebraic equations in [formula omitted

A method and the corresponding algorithm of finding residue integrals for systems of non-algebraic equations containing analytic functions are presented. Such integrals are connected to the power sums of roots for a certain system of equations. The described approach can be used for developing methods for the elimination of unknowns from systems of non-algebraic equations. It is shown how the obtained results can be used for calculating sums of multidimensional series.

Evaluation of power sums of roots for systems of non-algebraic equations in ℂ n

The goal of this paper is the evaluation of power sums of roots for systems of nonalgebraic equations consisting of entire or meromorphic functions of finite orders of growth. These power sums are connected with some residue integrals different from the Grothendieck residues. As an application we evaluate sums of certain multiple series.

An algorithm for calculating power sums of roots for a class of systems of nonlinear equations

An algorithm for calculating power sums of roots for a class of systems of nonlinear non-algebraic equations is presented. The algorithm is based on multidimensional recurrent formulas obtained earlier by the author.

Power sums of roots of a nonlinear system

For a system of meromorphic functions f = (f 1, …, fn ) in n , an explicit formula is given for evaluating negative power sums of the roots of the nonlinear system f (z) = 0. Under reasonable assumptions on the system, we introduce the concept of a zeta-function associated with the system. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in n .

Fast computation of special resultants

We propose fast algorithms for computing composed products and composed sums, as well as diamond products of univariate polynomials. These operations correspond to special multivariate resultants, that we compute using power sums of roots of polynomials, by means of their generating series.

Evaluation and optimization of perceptually-based ASR front-end

Several recently proposed automatic speech recognition (ASR) front-ends are experimentally compared in speaker-dependent, speaker-independent (or cross-speaker) recognition. The perceptually based linear predictive (PLP) front-end, with the root-power sums (RPS) distance measure, yields generally the highest accuracies, especially in cross-speaker recognition., It is experimentally shown that one can optimize the system and further improve recognition accuracy for speaker-independent recognition by controlling the distance measure's sensitivity to spectral peaks and the spectral tilt and by utilizing the speech dynamic features. For a digit vocabulary and five reference templates obtained with a clustering algorithm, the optimization improves recognition accuracy from 97% to 98.1%, with respect to the PL-PRPS front-end.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comparative study of ASR front-ends in noise

In automatic speech recognition (ASR) of speech corrupted by noise, the performance tends to deteriorate rapidly depending on the choice of analysis method and distance measure. In order to evaluate the recognition performance for several analysis methods and distance measures, a series of isolated word recognition experiments was performed. Analysis methods selected are critical-band filtering, perceptually based linear prediction (PLP), linear prediction (LP), and time synchronous linear prediction (SLP). The weighted Euclidean distance with different weightings [unity, root power sums (RPS), and exponential filtering] was applied in the cepstrum domain. Experiments were carried out for clean speech and for two noise conditions (white and low-pass filtered white, added to the clean speech) at different SNR ratios (25 to 5 dB), using an alphanumeric vocabulary (ten speakers). It is shown that improvements in robustness of the recognizer in noise can be achieved by a proper selection of analysis method and cepstral weights used in the front-end. Improvements are found over the RPS distance measure (previously shown to be useful in noise conditions with LP and PLP analyses) [B. Hanson and H. Wakita, Proceedings ICASSP 86 (IEEE, New York, 1986), pp. 757–760] by use of the general exponential lifter.

Evaluation of ASR front ends in speaker‐dependent and speaker‐independent recognition

This paper extends previous experiments of Tsuga and Hermansky [J. Acoust. Soc. Am. Suppl. 1 80, Sl8 (1986)]. Those experiments evaluated the effect of spectral model order, in automatic speech recognition (ASR), using a small alpha‐numeric data base. PLP (perceptually based linear predictive) and LP (linear predictive) analyses were compared, using a cepstral and RPS (root power sums) metric. Those experiments dealing with a bigger data base were validated (104 words, ten speakers). PLP RPS front end is compared with about ten other ASR front ends (LP ceptrum, LP RPS, critical band,…). Experiments were run at various different analysis model orders. Results of speaker‐dependent ASR show that the low‐dimensional PLP analysis is a good alternative to high‐dimensional LP or filter bank analysis. The index‐weighted metric improves the recognition accuracy, making the recognition results more uniform across the speakers. The speaker‐independent experiments (which use the templates of one male and one female speaker as references) confirm the superior performance of the PLP method for extracting speaker‐independent information. Most of the errors are on the consonants; some improvements on the recognition process are being investigated.

On the performance of the quefrency-weighted cepstral coefficients in vowel recognition

From a number of linear prediction parametric representations each of which furnishes equivalent information about the linear predictor, the cepstral coefficients representation is known to provide the best speech recognition performance. Since the cepstral coefficients of a stable all-pole filter are inversely proportional to their quefrencies, these coefficients are multipled by their respective quefrencies. The quefrency-weighted cepstral coefficients (also known as the root-power sums) are studied as to their effectiveness in a vowel recognition experiment and found to perform better than the cepstral coefficients with a Euclidean distance measure.

Power Sums of Roots

Power Sums of Roots

Power Sums of Roots

Power Sums of Roots