Backward error analysis of Neville elimination

Abstract Neville elimination is a useful alternative to Gauss elimination in order to study many properties of totally positive matrices. In this paper we perform a backward error analysis of that elimination procedure. In the case of totally positive matrices, the error bounds are similar to those obtained previously by other authors for Gauss elimination.

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

[2]  Juan Manuel Peña,et al.  Total positivity, QR factorization, and Neville elimination , 1993 .

[3]  Juan Manuel Peña,et al.  Totally positive bases for shape preserving curve design and optimality of B-splines , 1994, Comput. Aided Geom. Des..

[4]  Juan Manuel Peña,et al.  On the characterization of almost strictly totally positive matrices , 1995, Adv. Comput. Math..

[5]  Sankatha Prasad Singh,et al.  Approximation Theory, Wavelets and Applications , 1995 .

[6]  K. A. Gallivan,et al.  Parallel Algorithms for Dense Linear Algebra Computations , 1990, SIAM Rev..

[7]  T. Andô.  Totally positive matrices , 1987 .

[8]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[9]  C. D. Boor,et al.  Backward error analysis for totally positive linear systems , 1976 .

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

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

[12]  Juan Manuel Peña,et al.  Least supported bases and local linear independence , 1994 .

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

[14]  N. Higham.  Bounding the error in Gaussian Elimination for Tridiagonal systems , 1990 .

[15]  Juan Manuel Peña,et al.  Scaled pivoting in Gauss and Neville elimination for totally positive systems , 1993 .

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

[17]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[18]  C. D. Boor,et al.  Total Positivity of the Spline Collocation Matrix. , 1973 .

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

[20]  Gene H. Golub,et al.  Matrix computations , 1983 .

[21]  J. M. Peña,et al.  Neville Elimination and Approximation Theory , 1995 .