On the numerical computation of the LMM's coefficients

AIP Conference Proceedings

Volumn 936, Issue , 2007, Pages 596-599

  Aceto, Lidia ^a   Sestini, Alessandra ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Bernstein polynomials; Conditioning; Linear multistep methods; Vandermonde matrix

Indexed keywords

EID: 35348820699     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.2790217     Document Type: Conference Paper

References (10)

1. B. A. Björk and V. Pereyra, Solution of Vandermonde systems of equations, Math. Comp. 24 no. 112, 893-903 (1970).
2. L. Brugnano and D. Trigiante, Solving differential problems by multistep initial and boundary value methods, Gordon and Breach Science Publishers, Amsterdam, 1998.
3. J. Cash, Stable recursions, Academic Press, London, 1979.
4. G. Dahlquist and A. Björk, Numerical Methods, Prentice-Hall Englewood Cliffs, 1974.
5. Farouki, R. T. and Goodman, T. N. T., On the optimal stability of the Bernstein basis, Math. Comp. 65 no. 216, 1553-1566, (1996).
6. G. Galimberti, V. Pereyra, Solving confluent Vandermonde systems of Hermite type, Numer. Math., 18, 44-60, (1971).
7. N. J. Higham, Fast solution of Vandermonde-like systems involving orthogonal polynomials, IMA J. Numer. Anal. 8, 473-486, (1988).
8. N. J. Higham, Stability analysis of algorithms for solving confluent Vandermonde-like systems, SIAM J. Matrix Anal. Appl. 11, No. 1, 23-41, (1990).
9. J. D. Lambert, Computational methods in ordinary differential equations, John Wiley and Sons, New York, 1973.
10. http://pitagora.dm.uniba.it/~mazzia/bvp/index.html