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Volumn 20, Issue 2, 1998, Pages 400-419

The Chebyshev polynomials of a matrix

Author keywords

Chebyshev polynomial of a matrix; Krylov subspace iteration; Matrix polynomial; Semidefinite programming

Indexed keywords


EID: 0032216889     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479896303739     Document Type: Article
Times cited : (35)

References (25)
  • 1
    • 0032327612 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability, and numerical results
    • F. ALIZADEH, J.-P. A. HAEBERLY, AND M. L. OVERTON, Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability, and numerical results, SIAM J. Optim., 8 (1998), pp. 746-768.
    • (1998) SIAM J. Optim. , vol.8 , pp. 746-768
    • Alizadeh, F.1    Haeberly, J.-P.A.2    Overton, M.L.3
  • 2
    • 0001030604 scopus 로고
    • Faber polynomials and the Faber series
    • J. H. CURTISS, Faber polynomials and the Faber series, Amer. Math. Monthly, 78 (1971), pp. 577-596.
    • (1971) Amer. Math. Monthly , vol.78 , pp. 577-596
    • Curtiss, J.H.1
  • 4
    • 0030172363 scopus 로고    scopus 로고
    • A MATLAB toolbox for Schwarz-Christoffel mapping
    • T. A. DRISCOLL, A MATLAB toolbox for Schwarz-Christoffel mapping, ACM Trans. Math. Software, 22 (1996), pp. 168-186.
    • (1996) ACM Trans. Math. Software , vol.22 , pp. 168-186
    • Driscoll, T.A.1
  • 5
    • 84941461128 scopus 로고
    • Über tschebyscheffsche polynome
    • G. FABER, Über Tschebyscheffsche Polynome, J. Reine Angew. Math., 150 (1920), pp. 79-106.
    • (1920) J. Reine Angew. Math. , vol.150 , pp. 79-106
    • Faber, G.1
  • 7
    • 0000580113 scopus 로고
    • GMRES/CR and Arnoldi/Lanczos as matrix approximation problems
    • A. GREENBAUM AND L. N. TREFETHEN, GMRES/CR and Arnoldi/Lanczos as matrix approximation problems, SIAM J. Sci. Comput., 15 (1994), pp. 359-368.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 359-368
    • Greenbaum, A.1    Trefethen, L.N.2
  • 10
    • 0031285899 scopus 로고    scopus 로고
    • Primal-dual path-following algorithms for semidefinite programming
    • R. D. C. MONTEIRO, Primal-dual path-following algorithms for semidefinite programming, SIAM J. Optim., 7 (1997), pp. 663-678.
    • (1997) SIAM J. Optim. , vol.7 , pp. 663-678
    • Monteiro, R.D.C.1
  • 11
    • 0003254248 scopus 로고
    • Interior point polynomial methods in convex programming
    • SIAM, Philadelphia, PA
    • Y. NESTEROV AND A. NEMIROVSKII, Interior Point Polynomial Methods in Convex Programming, Stud. Appl. Math. 13, SIAM, Philadelphia, PA, 1994.
    • (1994) Stud. Appl. Math. , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 12
    • 0032222088 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for self-scaled cones
    • Y. E. NESTEROV AND M. J. TODD, Primal-dual interior-point methods for self-scaled cones, SIAM J. Optim., 8 (1998), pp. 324-364.
    • (1998) SIAM J. Optim. , vol.8 , pp. 324-364
    • Nesterov, Y.E.1    Todd, M.J.2
  • 13
    • 0028695631 scopus 로고
    • Pseudospectra of the convection-diffusion operator
    • S. C. REDDY AND L. N. TREFETHEN, Pseudospectra of the convection-diffusion operator, SIAM J. Appl. Math., 54 (1994), pp. 1634-1649.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1634-1649
    • Reddy, S.C.1    Trefethen, L.N.2
  • 14
    • 0000186540 scopus 로고
    • Eigenvalues and pseudo-eigenvalues of toeplitz matrices
    • L. REICHEL AND L. N. TREFETHEN, Eigenvalues and pseudo-eigenvalues of Toeplitz matrices, Linear Algebra Appl., 169 (1992), pp. 153-185.
    • (1992) Linear Algebra Appl. , vol.169 , pp. 153-185
    • Reichel, L.1    Trefethen, L.N.2
  • 15
    • 0001396701 scopus 로고
    • A fast algorithm for linear complex Chebyshev approximations
    • P. T. P. TANG, A fast algorithm for linear complex Chebyshev approximations, Math. Comp., 51 (1988), pp. 721-739.
    • (1988) Math. Comp. , vol.51 , pp. 721-739
    • Tang, P.T.P.1
  • 16
    • 0032359979 scopus 로고    scopus 로고
    • On the Nesterov-Todd direction in semidefinite programming
    • M. J. TODD, K.-C. TOH, AND R. H. TÜTÜNCÜ, On the Nesterov-Todd direction in semidefinite programming, SIAM J. Optim., 8 (1998), pp. 769-796.
    • (1998) SIAM J. Optim. , vol.8 , pp. 769-796
    • Todd, M.J.1    Toh, K.-C.2    Tütüncü, R.H.3
  • 18
    • 0001953835 scopus 로고    scopus 로고
    • Calculation of pseudospectra by the Arnoldi iteration
    • K.-C. TOH AND L. N. TREFETHEN, Calculation of pseudospectra by the Arnoldi iteration, SIAM J. Sci. Comput., 17 (1996), pp. 1-15.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1-15
    • Toh, K.-C.1    Trefethen, L.N.2
  • 21
    • 0000992781 scopus 로고
    • Pseudospectra of matrices
    • D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK
    • L. N. TREFETHEN, Pseudospectra of matrices, in Numerical Analysis 1991, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK, 1992.
    • (1992) Numerical Analysis 1991
    • Trefethen, L.N.1
  • 23
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 24
    • 0002059690 scopus 로고
    • Extremal polynomials associated with a system of curves in the complex plane
    • H. WIDOM, Extremal polynomials associated with a system of curves in the complex plane, Adv. Math., 3 (1969), pp. 127-232.
    • (1969) Adv. Math. , vol.3 , pp. 127-232
    • Widom, H.1
  • 25
    • 0032081158 scopus 로고    scopus 로고
    • On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming
    • Y. ZHANG, On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming, SIAM J. Optim., 8 (1998), pp. 365-386.
    • (1998) SIAM J. Optim. , vol.8 , pp. 365-386
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.