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High-Order Exponentially Fitted Methods for Accurate Prediction of Milling Stability. [PDF]
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Algorithmic Applications in Management, 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)
W. Ding, K. 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)
W. Ding, K. Qiu
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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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Block Kronecker linearizations of matrix polynomials and their backward errors
Numerische Mathematik, 2017We introduce a new family of strong linearizations of matrix polynomials—which we call “block Kronecker pencils”—and perform a backward stability analysis of complete polynomial eigenproblems.
F. Dopico +3 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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