Growth factors of pivoting strategies associated with Neville elimination

Neville elimination is a direct method for solving linear systems. Several pivoting strategies for Neville elimination, including pairwise pivoting, are analyzed. Bounds for two different kinds of growth factors are provided. Finally, an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed using random matrices.

[1]  Danny C. Sorensen,et al.  Analysis of Pairwise Pivoting in Gaussian Elimination , 1985, IEEE Transactions on Computers.

[2]  Alexander Tiskin Communication-efficient parallel generic pairwise elimination , 2007, Future Gener. Comput. Syst..

[3]  Jesús Vigo-Aguiar,et al.  On the stability of exponential fitting BDF algorithms , 2005 .

[4]  Jesús Vigo-Aguiar,et al.  A numerical algorithm for singular perturbation problems exhibiting weak boundary layers , 2003 .

[5]  Alan George,et al.  On the growth factor in Gaussian elimination for generalized Higham matrices , 2002, Numer. Linear Algebra Appl..

[6]  L. Trefethen,et al.  Average-case stability of Gaussian elimination , 1990 .

[7]  Juan Manuel Peña,et al.  Total positivity and Neville elimination , 1992 .

[8]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[9]  Rosemary A. Renaut,et al.  Stability of a Pivoting Strategy for Parallel Gaussian Elimination , 2001 .

[10]  Juan Manuel Peña,et al.  A matricial description of Neville elimination with applications to total positivity , 1994 .

[11]  Pedro Alonso,et al.  Iterative refinement for Neville elimination , 2009, Int. J. Comput. Math..

[12]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[13]  Charles A. Micchelli,et al.  Total positivity and its applications , 1996 .

[14]  Juan R. Torregrosa,et al.  A Totally Positive Factorization of Rectangular Matrices by the Neville Elimination , 2004, SIAM J. Matrix Anal. Appl..

[15]  Vicente Cortés,et al.  Growth factor and expected growth factor of some pivoting strategies , 2006 .

[16]  Juan Manuel Peña,et al.  Neville elimination: an efficient algorithm with application to chemistry , 2010 .

[17]  José Ranilla,et al.  Neville elimination: a study of the efficiency using checkerboard partitioning , 2004 .

[18]  James Demmel,et al.  The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System , 2005, SIAM J. Matrix Anal. Appl..

[19]  Juan Manuel Peña,et al.  Backward error analysis of Neville elimination , 1997 .