Results 11 to 20 of about 2,914,259 (200)
Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Matrix-valued Gegenbauer-type polynomials are investigated. The main results of the paper are stated in Sections 2 and 3. In Section 2 the matrix-valued weight functions \(W^{(\nu)}(x)\), which are analogues of the weight function for the Gegenbauer polynomials \(C^{(\nu)}_n(x)\) are introduced: \(W^{(\nu)}(x)= (1-x^2)^{\nu-1/2}W^{(\nu)}_{\mathrm{pol}}(
Koelink, Erik +2 more
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Operational matrix based on Genocchi polynomials for solution of delay differential equations
Ain Shams Engineering Journal, 2018 In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equations, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on ...
Abdulnasir Isah, Chang Phang
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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Mathematics, 2023 In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and ...
Dionisio Peralta +2 more
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Root polynomials and their role in the theory of matrix polynomials
Linear Algebra and its Applications, 2020 We develop a complete and rigorous theory of root polynomials of arbitrary matrix polynomials, i.e., either regular or singular, and study how these vector polynomials are related to the spectral properties of matrix polynomials.
F. Dopico, V. Noferini
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Triangularizing Quadratic Matrix Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2013 We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable ...
Tisseur, Françoise, Zaballa, Ion
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Computation, 2020 In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function.
Chang Phang +2 more
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On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach
Axioms, 2022 In this paper, we consider an approach based on the elementary matrix theory. In other words, we take into account the generalized Gaussian Fibonacci numbers. In this context, we consider a general tridiagonal matrix family.
Fatih Yılmaz, Mustafa Özkan
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Quasi-Polynomials of Capelli. II [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 This paper observes the continuation of the study of a certain kind of polynomials of type Capelli (Capelli quasi-polynomials) belonging to the free associative algebra F{X S Y } considered over an arbitrary field F and generated by two disjoint ...
Stepan Yuryevich Antonov +1 more
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On the bivariate Padovan polynomials matrix [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate ...
Orhan Dişkaya +2 more
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Block minimal bases ℓ-ifications of matrix polynomials [PDF]
Linear Algebra and its Applications, 2018 The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil, known as a strong linearization.
F. Dopico, J. P'erez, P. Van Dooren
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