Results 51 to 60 of about 31,852 (174)
On Chebyshev Polynomials of Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 The $m$th Chebyshev polynomial of a square matrix $A$ is the monic polynomial that minimizes the matrix 2-norm of $p(A)$ over all monic polynomials $p(z)$ of degree $m$. This polynomial is uniquely defined if $m$ is less than the degree of the minimal polynomial of $A$.
Liesen, Jörg +2 more
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Chebyshev polynomials and their some interesting applications
Advances in Difference Equations, 2017 The main purpose of this paper is by using the definitions and properties of Chebyshev polynomials to study the power sum problems involving Fibonacci polynomials and Lucas polynomials and to obtain some interesting divisible properties.
Chen Li, Zhang Wenpeng
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Total characters and Chebyshev polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The total character τ of a finite group G is defined as the sum of all the irreducible characters of G. K. W. Johnson asks when it is possible to express τ as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson′s question for all finite dihedral groups.
Eirini Poimenidou, Homer Wolfe
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Complex Factorizations of the Lucas Sequences via Matrix Methods
Journal of Applied Mathematics, 2014 Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev ...
Honglin Wu
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Determinants of Tridiagonal and Circulant Matrices Special Form by Chebyshev Polynomials
JTAM (Jurnal Teori dan Aplikasi Matematika)Along with the development of science, many researchers have found new methods to determine the determinant of a matrix of more than three orders.
Nurliantika Nurliantika +2 more
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A New Identity Involving the Chebyshev Polynomials
Mathematics, 2018 In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev ...
Yixue Zhang, Zhuoyu Chen
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Ain Shams Engineering Journal, 2018 In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method ...
Basim Albuohimad +2 more
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Boundary Value ProblemsThis paper presents two operational matrices. The first one represents integer-order derivatives of the modified shifted Chebyshev polynomials of the second kind.
M. Abdelhakem +3 more
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Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations
International Journal of Mathematics and Mathematical Sciences, 2011 We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in
Ahmad Imani, Azim Aminataei, Ali Imani
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Mathematics, 2018 In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of
Taekyun Kim +3 more
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