The Solution of Almost Block Diagonal Linear Systems Arising in Spline Collocation aT Gaussian Points with Monomial Basis Functions

ACM Transactions on Mathematical Software (TOMS)

Volumn 18, Issue 2, 1992, Pages 193-204

  Majaess, Gouad ^a   Keast, Patrick ^a   Fairweather, Graeme ^b   Bennett, Karin R ^c  

^a DALHOUSIE UNIVERSITY   (Canada)

^b UNIVERSITY OF KENTUCKY   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

almost block diagonal systems; alternate column and row pivoting; implicit Runge Kutta methods; monomial spline bases; multiple shooting; spline collocation at Gaussian points

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SOFTWARE; DIFFERENTIAL EQUATIONS; LINEAR ALGEBRA; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS;

ALMOST BLOCK DIAGONAL LINEAR SYSTEMS; GAUSSIAN POINTS; IMPLICIT RUNGE KUTTA METHODS; MONOMIAL BASIS FUNCTIONS; MULTIPLE SHOOTING; PIECEWISE POLYNOMIALS; SPLINE COLLOCATION;

BOUNDARY VALUE PROBLEMS;

EID: 0026875275     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/146847.146926     Document Type: Article

References (15)

1. ASCHEE, U., CHRISTIANSEN, J., AND RUSSELL, R. D. Collocation software for boundary-value ODEs. ACM Trans. Math. Softw. 7, 2 (1981), 209-229.
2. ASCHER, U., PRUESS, S., AND RUSSELL, R. D. On spline basis selection for solving differential equations. SIAM J. Numer. Anal. 20, 1 (1983), 121-142.
3. BADER, G., AND ASCHER, U. A new basis implementation for a mixed order boundary value ODE solver. SIAM J. Sci. Stat. Comput. 8, 4 (1987), 483-500.
4. DE BOOR, C. A Practical Guide to Splines. Springer-Verlag, 1978.
5. DE BOOR, C., AND WEISS, R. SOLVEBLOK: A package for solving almost block diagonal linear systems. ACM Trans. Math. Softw. 6, 1 (1980), 80-87.
6. DIAZ, J. C., FAIRWEATHER, G. AND KEAST, P. FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. ACM Trans. Math. Softw. 9, 3 (1983), 358-375.
7. DIAZ, J. C., FAIRWEATHER, G. AND KEAST, P. COLROW and ARCECO: FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. ACM Trans. Math. Softw. 9, 3 (1983), 376-380.
8. DONGARRA, J. J., MOLER, C. B., BUNCH, J. R., AND STEWART, G. W. LINPACK User's Guide. Society for Industrial and Applied Mathematics, Philadelphia, 1979.
9. LENTINI, S., OSBORNE, S. R., AND RUSSELL, R. D. The close relationship between methods for solving two-point boundary value problems SIAM J. Numer. Anal. 22, 2 (1985), 280-309.
10. MAJAESS, F., AND KEAST, P. Algorithms for the solution of linear systems arising from monomial spline basis functions. Tech. Rep. 1987CS-11, Dept. of Mathematics, Statistics and Computing Science, Dalhousie Univ., Halifax, Canada
11. MAJAESS, F., KEAST, P., FAIRWEATHER, G., AND BENNETT, K. R Fortran packages for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions Tech. Rep. CCS-90-3, Center for Computational Sciences, Univ. of Kentucky, Lexington, Kentucky.
12. MAJAESS, F., KEAST, P., FAIRWEATHER, G., AND BENNETT, K. R Algorithm XXX: ABDPACK and ABBPACK-Fortran programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. ACM Trans. Math. Soft. Submitted.
13. MUIR, P. J. Implicit Runge-Kutta methods for two-point boundary value problems. Ph D. Thesis, Univ of Toronto, Tech. Rep. 175/84, Dept. of Computer Science, Univ. of Toronto, Toronto, Ontario, Canada, M5S 4A7.
14. STOER, J., AND BULIRSCH, R. Introduction to Numerical Analysis, Springer-Verlag, 1980.
15. VARAH, J. M Alternate row and column elimination for solving certain linear systems. SIAM J. Numer. Anal. 13, 1, (1976), 71-75.