Numerical aspects of the coeffcient computation for LMMs

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 3, Issue 3-4, 2008, Pages 181-191

  Aceto, L ^a   Sestini, A ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Bernstein polynomials; Bj rk Pereyra algorithm; Boundary value methods; Conditioning; Linear multistep methods; Vandermonde matrix

Indexed keywords

EID: 72949099606     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. L. Aceto and A. Sestini, On the numerical computation of the LMM's coefficients, (Editors: E. Simos, G. Psihoyios and C. Tsitouras), Numerical Analysis and Applied Mathematics, AIP 596-599(2007).
2. L. Aceto and D. Trigiante, The matrices of Pascal and other greats. Amer. Math. Monthly, 108 no. 3, 232-245 (2001).
3. B.A. Björk and V. Pereyra, Solution of Vandermonde systems of equations. Math. Comp., 24 no. 112, 893-903 (1970).
4. L. Brugnano and D. Trigiante, Solving differential problems by multistep initial and boundary value methods. Gordon and Breach Science Publishers, Amsterdam, 1998.
5. C. de Boor, A practical guide to splines, Revised Edition Springer-Verlag, New York, Berlin, Heidelberg, 2001.
6. G. Farin, Curves and surfaces for computer aided geometric design, Third Edition, Academic Press, Inc., San Diego, 1993.
7. R.T. Farouki and T.N.T. Goodman, On the optimal stability of the Bernstein basis, Math. Comp., 65 no. 216, 1553-1566 (1996).
8. N. J. Higham, Error analysis of the Björk-Pereyra algorithms for solving Vandermonde systems, Numer. Math., 50 613-632(1987).
9. N. J. Higham, Stability analysis of algorithms for solving confluent Vandermonde-like systems, SIAM J. Matrix Anal. Appl., 11 No. 1, 23-41(1990).
10. F. Mazzia, TOM code. Available online at: http://pitagora.dm.uniba.it/~mazzia/bvp/ index.html
11. F. Mazzia, A. Sestini and D. Trigiante, B-spline linear multistep methods and their continuous extensions, Siam J. of Numerical Analysis, 44 No. 5, 1954-1973(2006).
12. F. Mazzia, A. Sestini and D. Trigiante, BS linear multistep methods on non-uniform meshes, JNAIAM, 1 131-144(2006).
13. F. Mazzia, A. Sestini and D. Trigiante, The continuous extension of the BS linear multistep methods on non-uniform meshes, in press on APNUM.