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Volumn 56, Issue 8, 2006, Pages 1077-1091

Computing real roots of a polynomial in Chebyshev series form through subdivision

Author keywords

Chebyshev polynomials; Rootfinding

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; INTERPOLATION; NUMERICAL METHODS; POLYNOMIALS; ROBUSTNESS (CONTROL SYSTEMS);

EID: 33744519285     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2005.09.007     Document Type: Article
Times cited : (24)

References (19)
  • 1
    • 0000944835 scopus 로고
    • A fast algorithm for the evaluation of Legendre expansions
    • Alpert B.A., and Rokhlin V. A fast algorithm for the evaluation of Legendre expansions. SIAM J. Sci. Comput. 12 (1991) 158-179
    • (1991) SIAM J. Sci. Comput. , vol.12 , pp. 158-179
    • Alpert, B.A.1    Rokhlin, V.2
  • 2
    • 6344220010 scopus 로고    scopus 로고
    • An extension of Matlab to continuous functions and operators
    • Battles Z., and Trefethen L.N. An extension of Matlab to continuous functions and operators. SIAM J. Sci. Comput. 25 (2004) 1743-1770
    • (2004) SIAM J. Sci. Comput. , vol.25 , pp. 1743-1770
    • Battles, Z.1    Trefethen, L.N.2
  • 4
    • 0344095828 scopus 로고
    • Butterworths Scientific Publications, London
    • Booth A.D. Numerical Methods (1955), Butterworths Scientific Publications, London
    • (1955) Numerical Methods
    • Booth, A.D.1
  • 5
    • 0345708608 scopus 로고
    • A Chebyshev polynomial interval-searching method ("Lanczos economization") for solving a nonlinear equation with application to the nonlinear eigenvalue problem
    • Boyd J.P. A Chebyshev polynomial interval-searching method ("Lanczos economization") for solving a nonlinear equation with application to the nonlinear eigenvalue problem. J. Comput. Phys. 118 (1995) 1-8
    • (1995) J. Comput. Phys. , vol.118 , pp. 1-8
    • Boyd, J.P.1
  • 7
    • 0344033726 scopus 로고    scopus 로고
    • Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding
    • Boyd J.P. Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding. SIAM J. Numer. Anal. 40 (2002) 1666-1682
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1666-1682
    • Boyd, J.P.1
  • 8
    • 14844347156 scopus 로고    scopus 로고
    • A review of high-order methods for incompressible fluid flow by M.O. Deville, P.F. Fischer and E.H. Mund
    • Boyd J.P. A review of high-order methods for incompressible fluid flow by M.O. Deville, P.F. Fischer and E.H. Mund. SIAM Rev. 46 (2004) 151-157
    • (2004) SIAM Rev. , vol.46 , pp. 151-157
    • Boyd, J.P.1
  • 9
    • 33744535250 scopus 로고    scopus 로고
    • J.P. Boyd, Computing the zeros of a Fourier series or trigonometric polynomial: matrix eigenvalue and subdivision algorithms, SIAM Rev. (2005), submitted for publication
  • 10
    • 33644594466 scopus 로고    scopus 로고
    • Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves
    • Boyd J.P. Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Appl. Math. Comput. 174 2 (2006) 1642-1658
    • (2006) Appl. Math. Comput. , vol.174 , Issue.2 , pp. 1642-1658
    • Boyd, J.P.1
  • 11
    • 33744510674 scopus 로고    scopus 로고
    • J.P. Boyd, D.H. Gally, 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. (2005), submitted for publication
  • 12
    • 33750187718 scopus 로고    scopus 로고
    • D.M. Day, L. Romero, Roots of polynomials expressed in terms of orthogonal polynomials, SIAM J. Numer. Anal. (2005), submitted for publication
  • 13
    • 0006616766 scopus 로고
    • Remarks on algorithms to find roots of polynomials
    • Goedecker S. Remarks on algorithms to find roots of polynomials. SIAM J. Sci. Comput. 15 (1994) 1059-1063
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1059-1063
    • Goedecker, S.1
  • 14
    • 0003398168 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ Reprinted by Dover, 1988
    • Lanczos C. Applied Analysis (1956), Prentice-Hall, Englewood Cliffs, NJ Reprinted by Dover, 1988
    • (1956) Applied Analysis
    • Lanczos, C.1
  • 15
    • 0031169815 scopus 로고    scopus 로고
    • Solving a polynomial equation: Some history and recent progress
    • Pan V.Y. Solving a polynomial equation: Some history and recent progress. SIAM Rev. 39 (1997) 187-220
    • (1997) SIAM Rev. , vol.39 , pp. 187-220
    • Pan, V.Y.1
  • 16
    • 0035892557 scopus 로고    scopus 로고
    • An algorithm for finding all solutions of a nonlinear system
    • Smiley M.W., and Chun C. An algorithm for finding all solutions of a nonlinear system. J. Comput. Appl. Math. 137 (2001) 293-315
    • (2001) J. Comput. Appl. Math. , vol.137 , pp. 293-315
    • Smiley, M.W.1    Chun, C.2
  • 19
    • 34250946236 scopus 로고
    • Randbermerkungen zu Hauptproblem der Mathematik, II. Fundamentalsatz der Algebra and Grundlagen der Mathematik
    • Weyl H. Randbermerkungen zu Hauptproblem der Mathematik, II. Fundamentalsatz der Algebra and Grundlagen der Mathematik. Math. Z. 20 (1924) 131-151
    • (1924) Math. Z. , vol.20 , pp. 131-151
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.