메뉴 건너뛰기




Volumn 199, Issue 1-2, 2008, Pages 185-206

Gauss-arnoldi quadrature for 〈(zI - A)-1φ, φ〉 and rational padé-type approximation for Markov-type functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 44449170494     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2008v199n02ABEH003915     Document Type: Article
Times cited : (3)

References (57)
  • 1
    • 0002807741 scopus 로고
    • The principle of minimized iterations in the solution of the matrix eigenvalue problem
    • W. E. Arnoldi, "The principle of minimized iterations in the solution of the matrix eigenvalue problem", Quart. Appl. Math. 9 (1951), 17-29.
    • (1951) Quart. Appl. Math , vol.9 , pp. 17-29
    • Arnoldi, W.E.1
  • 3
    • 0013091802 scopus 로고
    • The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems
    • Pite Havsbad, Sweden
    • A. Ruhe, "The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems", Matrix pencils (Pite Havsbad, Sweden, 1982),
    • (1982) Matrix pencils
    • Ruhe, A.1
  • 4
    • 85164632489 scopus 로고    scopus 로고
    • Proceedings of the Conference, Lect. Notes in Math., 973, Springer-Verlag, Berlin-Heidelberg 1982, pp. 104-120.
    • Proceedings of the Conference, Lect. Notes in Math., vol. 973, Springer-Verlag, Berlin-Heidelberg 1982, pp. 104-120.
  • 5
    • 49149143501 scopus 로고
    • Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
    • Y. Saad, "Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices", Linear Algebra Appl. 34 (1980), 269-295.
    • (1980) Linear Algebra Appl , vol.34 , pp. 269-295
    • Saad, Y.1
  • 6
    • 84966222159 scopus 로고
    • Krylov subspace methods for solving large unsymmetric linear systems
    • Y. Saad, "Krylov subspace methods for solving large unsymmetric linear systems", Math. Comp. 37:155 (1981), 105-126.
    • (1981) Math. Comp , vol.37 , Issue.155 , pp. 105-126
    • Saad, Y.1
  • 7
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad and M. H. Schultz, "GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems", SIAM J. Sci. Statist. Comput. 7:3 (1986), 856-869.
    • (1986) SIAM J. Sci. Statist. Comput , vol.7 , Issue.3 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 8
    • 0001765691 scopus 로고
    • A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations
    • H. C. Elman, Y. Saad, and P. E. Saylor, "A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations", SIAM J. Sci. Statist. Comput. 7:3 (1986), 840-855.
    • (1986) SIAM J. Sci. Statist. Comput , vol.7 , Issue.3 , pp. 840-855
    • Elman, H.C.1    Saad, Y.2    Saylor, P.E.3
  • 9
    • 0012746776 scopus 로고
    • Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices
    • D. Ho, F. Chatelin, and M. Bennani, "Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices", RAIRO Modél. Math. Anal. Numér. 24:1 (1990), 53-65.
    • (1990) RAIRO Modél. Math. Anal. Numér , vol.24 , Issue.1 , pp. 53-65
    • Ho, D.1    Chatelin, F.2    Bennani, M.3
  • 10
    • 0000977352 scopus 로고
    • Hybrid Krylov methods for nonlinear systems of equations
    • P. N. Brown and Y. Saad, "Hybrid Krylov methods for nonlinear systems of equations", SIAM J. Sci. Statist. Comput. 11:3 (1990), 450-481.
    • (1990) SIAM J. Sci. Statist. Comput , vol.11 , Issue.3 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 11
    • 0001436426 scopus 로고
    • Iterative solution of linear equations in ODE codes
    • C. W. Gear and Y. Saad, "Iterative solution of linear equations in ODE codes", SIAM J. Sci. Statist. Comput. 4:4 (1983), 583-601.
    • (1983) SIAM J. Sci. Statist. Comput , vol.4 , Issue.4 , pp. 583-601
    • Gear, C.W.1    Saad, Y.2
  • 12
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov approximation methods
    • E. Gallopoulos and Y. Saad, "Efficient solution of parabolic equations by Krylov approximation methods", SIAM J. Sci. Statist. Comput. 13:5 (1992), 1236-1264.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , Issue.5 , pp. 1236-1264
    • Gallopoulos, E.1    Saad, Y.2
  • 13
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • M. Hochbruck and Ch. Lubich, "On Krylov subspace approximations to the matrix exponential operator", SIAM J. Numer. Anal. 34:5 (1997), 1911-1925.
    • (1997) SIAM J. Numer. Anal , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 14
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Y. Saad, "Analysis of some Krylov subspace approximations to the matrix exponential operator", SIMA J. Numer. Anal. 29:1 (1992), 209-228.
    • (1992) SIMA J. Numer. Anal , vol.29 , Issue.1 , pp. 209-228
    • Saad, Y.1
  • 15
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • M. Hochbruck, Ch. Lubich, and H. Selhofer, "Exponential integrators for large systems of differential equations", SIAM J. Sci. Comput. 19:5 (1998), 1552-1574.
    • (1998) SIAM J. Sci. Comput , vol.19 , Issue.5 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, C.2    Selhofer, H.3
  • 16
    • 0042970108 scopus 로고
    • Calculation of functions of unsymmetric matrices using Arnoldi's method
    • L. A. Knizhnerman, "Calculation of functions of unsymmetric matrices using Arnoldi's method", Zh. Vychisl. Mat. Mat. Fiz. 31:1 (1991), 5-16;
    • (1991) Zh. Vychisl. Mat. Mat. Fiz , vol.31 , Issue.1 , pp. 5-16
    • Knizhnerman, L.A.1
  • 17
    • 85164635594 scopus 로고
    • English transl
    • English transl. in USSR Comput. Math, and Math. Phys. 31:1 (1991), 1-9.
    • (1991) USSR Comput. Math, and Math. Phys , vol.31 , Issue.1-9 , pp. 1
  • 18
    • 85164644061 scopus 로고
    • Error bounds in Arnoldi's method: The case of a normal matrix
    • L. A. Knizhnerman, "Error bounds in Arnoldi's method: the case of a normal matrix", Zh. Vychisl. Mat. Mat. Fiz. 32:9 (1992), 1347-1360;
    • (1992) Zh. Vychisl. Mat. Mat. Fiz , vol.32 , Issue.9 , pp. 1347-1360
    • Knizhnerman, L.A.1
  • 19
    • 85164641866 scopus 로고
    • in Comput
    • English transl. in Comput. Math. Math. Phys. 32:9 (1992), 1199-1211.
    • (1992) Math. Math. Phys , vol.32 , Issue.9 , pp. 1199-1211
    • English transl1
  • 20
    • 85164638979 scopus 로고    scopus 로고
    • On adaptation of the Arnoldi method to the spectrum
    • Technical report, Schlumberger-Doll Research Report #EMG-001-96-03
    • L. Knizhnerman, On adaptation of the Arnoldi method to the spectrum, Technical report, Schlumberger-Doll Research Report #EMG-001-96-03, 1996.
    • (1996)
    • Knizhnerman, L.1
  • 21
    • 0033406968 scopus 로고    scopus 로고
    • Error bounds for the Arnoldi method: A set of extreme eigenpairs
    • L. Knizhnerman, "Error bounds for the Arnoldi method: a set of extreme eigenpairs", Linear Algebra Appl. 296:1-3 (1999), 191-211.
    • (1999) Linear Algebra Appl , vol.296 , Issue.1-3 , pp. 191-211
    • Knizhnerman, L.1
  • 23
    • 85164633986 scopus 로고    scopus 로고
    • English transl., Transl. Math. Monogr., 92, Amer. Math. Soc., Providence, RI 1991.
    • English transl., Transl. Math. Monogr., vol. 92, Amer. Math. Soc., Providence, RI 1991.
  • 25
    • 0002949925 scopus 로고
    • (Markov), "Deux démonstrations de la convergence de certaines fractions
    • A. Markoff (Markov), "Deux démonstrations de la convergence de certaines fractions", Acta Math. 19:1 (1895), 93-104.
    • (1895) Acta Math , vol.19 , Issue.1 , pp. 93-104
    • Markoff, A.1
  • 26
    • 0003733525 scopus 로고
    • Encyclopedia Math. Appl, Cambridge Univ. Press, Cambridge
    • H. Stahl and V. Totik, General orthogonal polynomials, Encyclopedia Math. Appl., vol. 43, Cambridge Univ. Press, Cambridge 1992.
    • (1992) General orthogonal polynomials , vol.43
    • Stahl, H.1    Totik, V.2
  • 27
    • 33646802840 scopus 로고
    • On adaptation of the Lanczos method to the spectrum
    • Technical report, Schlumberger-Doll Research, Res. Note EMG-001-95-12
    • L. Knizhnerman, On adaptation of the Lanczos method to the spectrum, Technical report, Schlumberger-Doll Research, Res. Note EMG-001-95-12, 1995.
    • (1995)
    • Knizhnerman, L.1
  • 28
    • 0001471025 scopus 로고
    • On convergence of Padé approximants for some classes of meromorphic functions
    • A. A. Gončar, "On convergence of Padé approximants for some classes of meromorphic functions", Mat. Sb. 97(139):4(8) (1975), 607-629;
    • (1975) Mat. Sb , vol.97 , Issue.139 , pp. 607-629
    • Gončar, A.A.1
  • 29
    • 85164651152 scopus 로고
    • English transl
    • English transl. in Math. USSR-Sb. 26:4 (1975), 555-575.
    • (1975) Math. USSR-Sb , vol.26 , Issue.555-575 , pp. 4
  • 30
    • 0000256886 scopus 로고
    • On the asymptotics of the ratio of orthogonal polynomials
    • E. A. Rahmanov, "On the asymptotics of the ratio of orthogonal polynomials", Mat. Sb. 103(145):2(6) (1977), 237-252;
    • (1977) Mat. Sb , vol.103 , Issue.145 , pp. 237-252
    • Rahmanov, E.A.1
  • 31
    • 85040329641 scopus 로고
    • English transl
    • English transl. in Math. USSR-Sb. 32:2 (1977), 199-213.
    • (1977) Math. USSR-Sb , vol.32 , Issue.199-213 , pp. 2
  • 32
    • 0001340426 scopus 로고
    • On the asymptotics of the ratio of orthogonal polynomials. II
    • E. A. Rakhmanov, "On the asymptotics of the ratio of orthogonal polynomials. II", Mat. Sb. 118(160):1(5) (1982), 104-117;
    • (1982) Mat. Sb , vol.118 , Issue.160 , pp. 104-117
    • Rakhmanov, E.A.1
  • 33
    • 85164654770 scopus 로고
    • English transl
    • English transl. in Math. USSR-Sb. 46:1 (1983), 105-117.
    • (1983) Math. USSR-Sb , vol.46 , Issue.105-117 , pp. 1
  • 34
    • 0001526240 scopus 로고
    • The convergence of diagonal Padé approximants
    • E. A. Rahmanov, "The convergence of diagonal Padé approximants", Mat. Sb. 104(146):2(10) (1977), 271-291;
    • (1977) Mat. Sb , vol.104 , Issue.146 , pp. 271-291
    • Rahmanov, E.A.1
  • 35
    • 85164639979 scopus 로고
    • English transl
    • English transl. in Math. USSR-Sb. 33:2 (1977), 243-260.
    • (1977) Math. USSR-Sb , vol.33 , Issue.243-260 , pp. 2
  • 36
    • 44449090604 scopus 로고    scopus 로고
    • Padé approximants of meromorphic functions of Markov type
    • Russian
    • A. A. Gonchar and S. P. Suetin, "Padé approximants of meromorphic functions of Markov type", Sovr. Probl. Mat., vol. 5, 2004, pp. 3-67. (Russian)
    • (2004) Sovr. Probl. Mat , vol.5 , pp. 3-67
    • Gonchar, A.A.1    Suetin, S.P.2
  • 37
    • 0003163478 scopus 로고    scopus 로고
    • Padé approximants and efficient analytic continuation of a power series
    • S. P. Suetin, "Padé approximants and efficient analytic continuation of a power series", Uspekhi Mat. Nauk 57:1 (2002), 45-142;
    • (2002) Uspekhi Mat. Nauk , vol.57 , Issue.1 , pp. 45-142
    • Suetin, S.P.1
  • 38
    • 85164654580 scopus 로고    scopus 로고
    • in Russian
    • English transl. in Russian Math. Surveys 57:1 (2002), 43-141.
    • (2002) Math. Surveys , vol.57 , Issue.1 , pp. 43-141
    • English transl1
  • 39
    • 0002193404 scopus 로고    scopus 로고
    • Uniform convergence of Padé diagonal approximants for hyperelliptic functions
    • S. P. Suetin, "Uniform convergence of Padé diagonal approximants for hyperelliptic functions", Mat. Sb. 191:9 (2000), 81-114;
    • (2000) Mat. Sb , vol.191 , Issue.9 , pp. 81-114
    • Suetin, S.P.1
  • 40
    • 85164656350 scopus 로고    scopus 로고
    • English transl
    • English transl. in Sb. Math. 191:9 (2000), 1339-1373.
    • (2000) Sb. Math , vol.191 , Issue.1339-1373 , pp. 9
  • 41
    • 11144289850 scopus 로고    scopus 로고
    • Convergence of Chebyshëv continued fractions for elliptic functions
    • S. P. Suetin, "Convergence of Chebyshëv continued fractions for elliptic functions", Mat. Sb. 194:12 (2003), 63-92;
    • (2003) Mat. Sb , vol.194 , Issue.12 , pp. 63-92
    • Suetin, S.P.1
  • 42
    • 85164633160 scopus 로고    scopus 로고
    • English transl
    • English transl. in Sb. Math. 194:12 (2003), 1807-1835.
    • (2003) Sb. Math , vol.194 , Issue.1807-1835 , pp. 12
  • 44
    • 22944489601 scopus 로고    scopus 로고
    • Quadrature rules based on the Arnoldi process
    • D. Calvetti, S.-M. Kim, and L. Reichel, "Quadrature rules based on the Arnoldi process", SIAM J. Matrix Anal. Appl. 26:3 (2005), 765-781.
    • (2005) SIAM J. Matrix Anal. Appl , vol.26 , Issue.3 , pp. 765-781
    • Calvetti, D.1    Kim, S.-M.2    Reichel, L.3
  • 46
    • 85164632999 scopus 로고    scopus 로고
    • Proceedings of the NATO Advanced Study Institute, NATO Adv. Sci. Inst. Ser. E Appl. Sci., 232, Kluwer Acad. Publ., Dordrecht 1993, pp. 377-380.
    • Proceedings of the NATO Advanced Study Institute, NATO Adv. Sci. Inst. Ser. E Appl. Sci., vol. 232, Kluwer Acad. Publ., Dordrecht 1993, pp. 377-380.
  • 47
    • 0000450702 scopus 로고
    • A Fotran 90-based multiprecision system
    • D.H. Bailey, "A Fotran 90-based multiprecision system", ACM Trans. Math. Software 21:4 (1995), 379-387.
    • (1995) ACM Trans. Math. Software , vol.21 , Issue.4 , pp. 379-387
    • Bailey, D.H.1
  • 48
    • 0004057553 scopus 로고
    • McGraw-Hill, New York-Düsseldorf-Johannesburg
    • W. Rudin, Functional analysis, McGraw-Hill, New York-Düsseldorf-Johannesburg 1973.
    • (1973) Functional analysis
    • Rudin, W.1
  • 49
    • 0030242188 scopus 로고    scopus 로고
    • Convergence rates of Padé and Padé-type approximants
    • A. Ambroladze and H. Wallin, "Convergence rates of Padé and Padé-type approximants", J. Approx. Theory 86:3 (1996), 310-319.
    • (1996) J. Approx. Theory , vol.86 , Issue.3 , pp. 310-319
    • Ambroladze, A.1    Wallin, H.2
  • 50
    • 85164653397 scopus 로고    scopus 로고
    • H. S. Shapiro, The Schwarz function and its generalization to higher dimensions, Univ. Arkansas Lecture Notes Math. Sci., 9, Wiley, New York 1992.
    • H. S. Shapiro, The Schwarz function and its generalization to higher dimensions, Univ. Arkansas Lecture Notes Math. Sci., vol. 9, Wiley, New York 1992.
  • 52
    • 0000126692 scopus 로고
    • On exceptional sets of asymptotic relations for general orthogonal polynomials
    • A. Ambroladze, "On exceptional sets of asymptotic relations for general orthogonal polynomials", J. Approx. Theory 82:2 (1995), 257-273.
    • (1995) J. Approx. Theory , vol.82 , Issue.2 , pp. 257-273
    • Ambroladze, A.1
  • 53
    • 85164639067 scopus 로고    scopus 로고
    • M. He, The Faber polynomials for circular arcs, Mathematics of computation, 1943-1993: a half- century of computational mathematics (Vancouver, Canada 1993),
    • M. He, "The Faber polynomials for circular arcs", Mathematics of computation, 1943-1993: a half- century of computational mathematics (Vancouver, Canada 1993),
  • 54
    • 85164645284 scopus 로고    scopus 로고
    • Proc. Sympos. Appl. Math., 48, Amer. Math. Soc., Providence, RI 1994, pp. 301-304.
    • Proc. Sympos. Appl. Math., vol. 48, Amer. Math. Soc., Providence, RI 1994, pp. 301-304.
  • 55
    • 0003956970 scopus 로고
    • Addison-Wesley, Reading, MA
    • S. Lang, Algebra, Addison-Wesley, Reading, MA 1965.
    • (1965) Algebra
    • Lang, S.1
  • 56
    • 0004236492 scopus 로고
    • Matrix computations
    • Johns Hopkins Univ. Press, Baltimore, MD
    • G. H. Golub and Ch. F. van Loan, Matrix computations, Johns Hopkins Ser. Math. Sci., vol. 3, Johns Hopkins Univ. Press, Baltimore, MD 1989.
    • (1989) Johns Hopkins Ser. Math. Sci , vol.3
    • Golub, G.H.1    van Loan, C.F.2
  • 57
    • 34248528660 scopus 로고    scopus 로고
    • Adaptation of the Lanczos and Arnoldi methods to the spectrum, or why the two Krylov subspace methods are powerful
    • L. A. Knizhnerman, "Adaptation of the Lanczos and Arnoldi methods to the spectrum, or why the two Krylov subspace methods are powerful", Chebyshevskiǐ Sb. 3:2 (2002), 141-164.
    • (2002) Chebyshevskiǐ Sb , vol.3 , Issue.2 , pp. 141-164
    • Knizhnerman, L.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.