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Volumn 42, Issue 2, 2002, Pages 393-407

On generating discrete orthogonal bivariate polynomials

Author keywords

Bivariate interpolation; Bivariate polynomial; Curve fitting; Lanczos algorithm; Least squares approximation; Slowly growing length of the recurrence

Indexed keywords


EID: 0042379785     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021907210628     Document Type: Article
Times cited : (9)

References (24)
  • 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
  • 2
    • 0012584237 scopus 로고
    • Polynomial interpolation in several variables
    • R. DeMillo and J. R. Rice, eds., Plenum Press, New York
    • C. de Boor, Polynomial interpolation in several variables, Studies in Computer Science, R. DeMillo and J. R. Rice, eds., Plenum Press, New York, 1994, pp. 87-119.
    • (1994) Studies in Computer Science , pp. 87-119
    • De Boor, C.1
  • 3
    • 84968521926 scopus 로고
    • Computational aspects of polynomial interpolation in several variables
    • C. de Boor and A. Ron, Computational aspects of polynomial interpolation in several variables, Math. Comp., 58 (1992), 705-727.
    • (1992) Math. Comp. , vol.58 , pp. 705-727
    • De Boor, C.1    Ron, A.2
  • 5
    • 0041710450 scopus 로고    scopus 로고
    • On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules, I
    • G. Dahlquist, On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules, I, BIT, 37 (1997), pp. 256-295.
    • (1997) BIT , vol.37 , pp. 256-295
    • Dahlquist, G.1
  • 6
    • 84966217951 scopus 로고
    • Reorthogonalization and Stable Algorithms Updating the Gram-Schmidt QR Factorization
    • J. W. Daniel, W. B. Gragg, L. Kaufman, and G. W. Stewart, Reorthogonalization and Stable Algorithms Updating the Gram-Schmidt QR Factorization, Math. Comp., 30 (1976), no. 136, 772-795.
    • (1976) Math. Comp. , vol.30 , Issue.136 , pp. 772-795
    • Daniel, J.W.1    Gragg, W.B.2    Kaufman, L.3    Stewart, G.W.4
  • 8
    • 0002099734 scopus 로고
    • Generation and use of orthogonal polynomials for data-fitting with digital computer
    • G. Forsythe, Generation and use of orthogonal polynomials for data-fitting with digital computer, J. Soc. Indust. Appl. Math., 5, (1957), pp. 74-88.
    • (1957) J. Soc. Indust. Appl. Math. , vol.5 , pp. 74-88
    • Forsythe, G.1
  • 9
    • 34249771766 scopus 로고
    • Least squares fitting of circles and ellipses
    • W. Gander, G. Golub, and R. Strebel, least squares fitting of circles and ellipses, BIT, 34 (1994), pp. 558-578.
    • (1994) BIT , vol.34 , pp. 558-578
    • Gander, W.1    Golub, G.2    Strebel, R.3
  • 10
    • 85014479701 scopus 로고    scopus 로고
    • Orthogonal Polynomials: Applications and Computations
    • Cambridge University Press, Cambridge
    • W. Gautschi, Orthogonal Polynomials: Applications and Computations, Acta Numerica 5 (1996), Cambridge University Press, Cambridge, pp. 45-119.
    • (1996) Acta Numerica , vol.5 , pp. 45-119
    • Gautschi, W.1
  • 11
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • G. H. Golub and J. H. Welsh, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221-230.
    • (1969) Math. Comp. , vol.23 , pp. 221-230
    • Golub, G.H.1    Welsh, J.H.2
  • 12
    • 0038621096 scopus 로고
    • Shape preserving interpolation by parametrically defined curves
    • T. N. Goodman and K. Unsworth, Shape preserving interpolation by parametrically defined curves, SIAM J. Numer. Anal., 25 (1988), pp. 1453-1465.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1453-1465
    • Goodman, T.N.1    Unsworth, K.2
  • 14
    • 0011031508 scopus 로고    scopus 로고
    • Orthogonal polyanalytic polynomials and normal matrices
    • to appear
    • M. Huhtanen, Orthogonal polyanalytic polynomials and normal matrices, Math. Comp., to appear.
    • Math. Comp.
    • Huhtanen, M.1
  • 15
    • 0036400874 scopus 로고    scopus 로고
    • Exclusion and inclusion regions for the eigenvalues of a normal matrix
    • to appear
    • M. Huhtanen and R. M. Larsen, Exclusion and inclusion regions for the eigenvalues of a normal matrix, SIAM J. Matrix Anal. Appl., to appear.
    • SIAM J. Matrix Anal. Appl.
    • Huhtanen, M.1    Larsen, R.M.2
  • 16
    • 0039546363 scopus 로고
    • On the calculation of Jacobi matrices
    • J. Kautsky and G. Golub, On the calculation of Jacobi matrices, Linear Algebra Appl., 52/53 (1983), pp. 439-455.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 439-455
    • Kautsky, J.1    Golub, G.2
  • 17
    • 0008909251 scopus 로고
    • The recursion formulas for orthogonal polynomials in n variables
    • M. A. Kowalski, The recursion formulas for orthogonal polynomials in n variables, SIAM J. Math. Anal., 13 (1982), pp. 309-315.
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 309-315
    • Kowalski, M.A.1
  • 19
    • 0025672456 scopus 로고
    • Algorithm 686: FORTRAN Subroutines for Updating the QR decomposition
    • L. Reichel and W. B. Gragg, Algorithm 686: FORTRAN Subroutines for Updating the QR decomposition, ACM Trans. Math. Software, 16 (1990), pp. 369-377.
    • (1990) ACM Trans. Math. Software , vol.16 , pp. 369-377
    • Reichel, L.1    Gragg, W.B.2
  • 20
    • 0031316402 scopus 로고    scopus 로고
    • Polynomial interpolation of minimal degree
    • T. Sauer, Polynomial interpolation of minimal degree, Numer. Math., 78 (1997), pp. 59-85.
    • (1997) Numer. Math. , vol.78 , pp. 59-85
    • Sauer, T.1
  • 22
    • 0043232750 scopus 로고    scopus 로고
    • Least squares fitting of circles and ellipses to measured data
    • G. A. Watson, Least squares fitting of circles and ellipses to measured data, BIT, 39 (1998), pp. 176-191.
    • (1998) BIT , vol.39 , pp. 176-191
    • Watson, G.A.1
  • 23
    • 0039424510 scopus 로고
    • Orthogonal polynomials in several variables
    • M. Weisfeld, Orthogonal polynomials in several variables, Numer. Math., 1 (1959), pp. 38-40.
    • (1959) Numer. Math. , vol.1 , pp. 38-40
    • Weisfeld, M.1
  • 24
    • 0347185339 scopus 로고
    • On multivariate orthogonal polynomials
    • Y. Xu, On multivariate orthogonal polynomials, SIAM J. Math. Anal., 24 (1993), pp. 783-794.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 783-794
    • Xu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.