zbMATH — the first resource for mathematics

Modular analysis of sequential solution methods for almost block diagonal systems of equations. (English) Zbl 1268.65039
Summary: Almost block diagonal systems of linear equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods. It also allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. The outcome of the analysis and implementation is to discover new methods that outperform a well-known method, a modification of which is, therefore, advocated.
65F05 Direct numerical methods for linear systems and matrix inversion
65F50 Computational methods for sparse matrices
Full Text: DOI
[1] P. Amodio, J. R. Cash, G. Roussos et al., “Almost block diagonal linear systems: sequential and parallel solution techniques, and applications,” Numerical Linear Algebra with Applications, vol. 7, no. 5, pp. 275-317, 2000. · Zbl 1051.65018
[2] J. C. Díaz, G. Fairweather, and P. Keast, “FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination,” ACM Transactions on Mathematical Software, vol. 9, no. 3, pp. 358-375, 1983. · Zbl 0516.65013 · doi:10.1145/356044.356053
[3] J. R. Cash and M. H. Wright, “A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation,” SIAM Journal on Scientific and Statistical Computing, vol. 12, no. 4, pp. 971-989, 1991. · Zbl 0727.65070 · doi:10.1137/0912052
[4] J. R. Cash, G. Moore, and R. W. Wright, “An automatic continuation strategy for the solution of singularly perturbed linear two-point boundary value problems,” Journal of Computational Physics, vol. 122, no. 2, pp. 266-279, 1995. · Zbl 0840.65084 · doi:10.1006/jcph.1995.1212
[5] W. H. Enright and P. H. Muir, “Runge-Kutta software with defect control for boundary value ODEs,” SIAM Journal on Scientific Computing, vol. 17, no. 2, pp. 479-497, 1996. · Zbl 0844.65064 · doi:10.1137/S1064827593251496
[6] P. Keast and P. H. Muir, “Algorithm 688: EPDCOL: a more efficient PDECOL code,” ACM Transactions on Mathematical Software, vol. 17, no. 2, pp. 153-166, 1991. · Zbl 0900.65270 · doi:10.1145/108556.108558 · www.acm.org
[7] R. W. Wright, J. R. Cash, and G. Moore, “Mesh selection for stiff two-point boundary value problems,” Numerical Algorithms, vol. 7, no. 2-4, pp. 205-224, 1994. · Zbl 0804.65077 · doi:10.1007/BF02140684
[8] D. C. Lam, Implementation of the box scheme and model analysis of diffusion-convection equations. [Ph.D. thesis], University of Waterloo: Waterloo, Ontario, Canada, 1974.
[9] J. M. Varah, “Alternate row and column elimination for solving certain linear systems,” SIAM Journal on Numerical Analysis, vol. 13, no. 1, pp. 71-75, 1976. · Zbl 0338.65016 · doi:10.1137/0713008
[10] H. B. Keller, “Accurate difference methods for nonlinear two-point boundary value problems,” SIAM Journal on Numerical Analysis, vol. 11, pp. 305-320, 1974. · Zbl 0282.65065 · doi:10.1137/0711028
[11] T. M. A. El-Mistikawy, “Solution of Keller’s box equations for direct and inverse boundary-layer problems,” AIAA journal, vol. 32, no. 7, pp. 1538-1541, 1994. · Zbl 0823.76065 · doi:10.2514/3.12226
[12] I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, UK, 1986. · Zbl 0604.65011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.