Results 51 to 60 of about 302,926 (303)
On zeros of paraorthogonal polynomials [PDF]
Proceedings of the American Mathematical Society, 2019 We prove some results concerning the behaviour of zeros of families of paraorthogonal polynomials on the unit circle. We establish an interlacing property of the zeros of some functions related to the paraorthogonal polynomials. Monotonicity with respect to a parameter is also discussed in detail.
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Laguerre-like methods for the simultaneous approximation of polynomial multiple zeros [PDF]
Yugoslav Journal of Operations Research, 2006 Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as ...
Petković Miodrag +2 more
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Finding the Zeros of a High-Degree Polynomial Sequence
Journal of Optimization, Differential Equations and Their Applications, 2021 A 1-parameter initial-boundary value problem for a linear spatially 1-dimensional homogeneous degenerate wave equation, posed in a space-time rectangle, in case of strong degeneracy, was reduced to a linear integro-differential equation of convolution ...
Vladimir L. Borsch, Peter I. Kogut
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Investigations in the Geometry of Polynomials [PDF]
, 2009 Because polynomial functions are completely determined by their roots, every property of a polynomial is affected when these roots change. Our research aims to further our understanding of how the distribution of a polynomial\u27s roots affects specjfic ...
Biegalle, Neil
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dynoGP: Deep Gaussian Processes for Dynamic System Identification
International Journal of Adaptive Control and Signal Processing, EarlyView.This work introduces a novel class of deep models for system identification, dynamical deep Gaussian processes, which combine the strengths of data‐driven methods, such as those based on neural network architectures, with the ability to output a probability distribution for uncertainty representation.
Alessio Benavoli +3 more
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On the Coefficients and Zeros of a Polynomial
Journal of Approximation Theory, 1999 In continuation of work by \textit{Q. I. Rahman} [Can. Math. Bull. 13, 541-542 (1970; Zbl 0205.37802)]\ and \textit{H. Alzer} [J. Approximation Theory 81, 421-424 (1995; Zbl 0837.30007)], the author offers two results on complex polynomials of the form \(p(z)=b_{0}+b_{1}z+b_{2}z^{2}+\cdots +b_{n}z^{n}\) with \(b_{0}=1.\) One states that the absolute ...
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On Polynomials with a Prescribed Zero
Journal of Mathematical Analysis and Applications, 1994 Let \(p(z)= \sum^ n_{j=0} a_ j z^ j\) be a polynomial of degree at most ``\(n\)'' vanishing at \(z= \zeta\) \((\zeta^{n+1}\neq 1)\). The authors use Lagrange's interpolation formula to prove that for every complex number \(\lambda\) and \(k= 0,1,2,\dots,n\), \[ \begin{multlined} a_ k= \bigl(1/k!(n- k+ 1)\bigr)\sum^{n-k}_{j=0} p^{(k)}\bigl(e^{2\pi ji/(n-
Dewan, K.K., Govil, N.K.
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Математичні СтудіїIn this paper, we establish some mathematical rules for determining the initial and terminal numbers of non-zero terms in any arbitrary polynomial. These rules lead to the definitions of index $s$ and reverse index $\hat{s}$ of a polynomial.
J. Banerjee, A. Banerjee
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A quantum search for zeros of polynomials [PDF]
, 2003 A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial.
Stefan Weigert, Weigert, S.
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Advanced Engineering Materials, EarlyView.Predicting extreme defects in additive manufacturing remains a key challenge limiting its structural reliability. This study proposes a statistical framework that integrates Extreme Value Theory with advanced process indicators to explore defect–process relationships and improve the estimation of critical defect sizes. The approach provides a basis for
Muhammad Muteeb Butt +8 more
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