Results 141 to 150 of about 543,835 (181)
Transversely isotropic hyperelastic laws for 2D FEM modeling of human thoracic spine ligaments. [PDF]
Sci RepWiczenbach T +5 more
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ON J-UNITARY MATRIX POLYNOMIALS
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ephremidze, Lasha +2 more
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Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials
Journal of Computational Physics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Wanzhen +5 more
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Orthogonal Matrix Laurent Polynomials
Mathematical Notes, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Afrika Matematika, 2013
The author introduces a new type of matrix polynomial, namely the Rice matrix polynomial \(H_n(A,B,z)\), where \(A,B\) are square complex matrices with \(B+kI\) invertible for all integers \(k\geq0\), by means of the hypergeometric matrix function. Its convergence properties, radius of convergence and an integral form are derived.
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The author introduces a new type of matrix polynomial, namely the Rice matrix polynomial \(H_n(A,B,z)\), where \(A,B\) are square complex matrices with \(B+kI\) invertible for all integers \(k\geq0\), by means of the hypergeometric matrix function. Its convergence properties, radius of convergence and an integral form are derived.
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2003
This chapter is devoted to proving a matrix version of Krein’s Theorem. The proof relies on methods that are different from those used in the scalar case.
Robert L. Ellis, Israel Gohberg
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This chapter is devoted to proving a matrix version of Krein’s Theorem. The proof relies on methods that are different from those used in the scalar case.
Robert L. Ellis, Israel Gohberg
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Solving Matrix Polynomial Equations
Cybernetics and Systems AnalysisMatrix equations and systems of matrix equations are widely used in problems of optimization of control systems, in mathematical economics. However, methods for solving them are developed only for the most popular matrix equations – the Riccati and Lyapunov equations, and there is no universal approach to solving problems of this class.
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2019
Given a square matrix \(M = (u_{ij})_{n \times n}\) and an m-order matrix polynomial \(f_m(M) = \sum _{k=0}^{m} a_k M^k = a_0 I + a_1M + a_2 M^2 + \cdots + a_m M^m\), if M is a dense matrix and is perturbed to become \(M'\) at a single entry, say \(u_{pq}\), a straightforward re-calculation of \(f_{m}(M')\) would require \(O(n^{\omega } \cdot \alpha (m)
Wei Ding, Ke Qiu
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Given a square matrix \(M = (u_{ij})_{n \times n}\) and an m-order matrix polynomial \(f_m(M) = \sum _{k=0}^{m} a_k M^k = a_0 I + a_1M + a_2 M^2 + \cdots + a_m M^m\), if M is a dense matrix and is perturbed to become \(M'\) at a single entry, say \(u_{pq}\), a straightforward re-calculation of \(f_{m}(M')\) would require \(O(n^{\omega } \cdot \alpha (m)
Wei Ding, Ke Qiu
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Numerical Range of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications, 1994Let \(A_ i\), \(i = 1, \dots, m\) be \(n \times n\) matrices with complex coefficients and consider the matrix polynomial \(P(\lambda) = \sum_{i=0}^ m A_ i \lambda^ i\). The numerical range of \(P(\lambda)\) is defined through \[ W \bigl( P(\lambda) \bigr) : = \{\mu \in \mathbb{C} \mid x^* P(\mu)x = 0 \quad \text{for some nonzero} \quad x \in \mathbb{C}
Li, Chi-Kwong, Rodman, Leiba
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1990
An overview is given of some classical and recent results concerning zeros of orthogonal matrix polynomials on the unit circle. The basic questions are: How these zeros are located in the complex plane? Conversely, what conditions on the location of the zeros of a given matrix polynomial ensure that the polynomial is orthogonal?
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An overview is given of some classical and recent results concerning zeros of orthogonal matrix polynomials on the unit circle. The basic questions are: How these zeros are located in the complex plane? Conversely, what conditions on the location of the zeros of a given matrix polynomial ensure that the polynomial is orthogonal?
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