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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 505 - 513 (9page)
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초록· 키워드
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In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is ex- hibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to nd a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indetermi- nates.
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참고문헌 (9)
참고문헌 신청
S. Barnett / 1981 / Congenial matrices / Linear Algebra Appl 41:277~298
D. S. Bernstein / 2009 / Matrix mathematics: theory, facts, and formulas / Princeton univer-sity press
J. P. Boyd / 2006 / Computing real roots of a polynomial in Chebyshev series form through subdivision / Appl. Numer. Math 56:1077~1091
J. P. Boyd / 2013 / Finding the zeros of a univariate equation: proxy rootfinders, Chebyshev interpolation, and the companion matrix / SIAM Rev 55(2):375~396
J. P. Boyd / 2007 / Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials / J. Comput. Appl. Math 205:281~295
D. S. Bernstein / 2009 / Matrix mathematics: theory, facts, and formulas / Princeton univer-sity press
J. P. Boyd / 2006 / Computing real roots of a polynomial in Chebyshev series form through subdivision / Appl. Numer. Math 56:1077~1091
J. P. Boyd / 2013 / Finding the zeros of a univariate equation: proxy rootfinders, Chebyshev interpolation, and the companion matrix / SIAM Rev 55(2):375~396
J. P. Boyd / 2007 / Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials / J. Comput. Appl. Math 205:281~295
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