Iterative refinement for Neville elimination

Neville elimination is an elimination procedure that is very useful when dealing with totally positive matrices. We provide a sufficient condition for the convergence of the iterative refinement using Neville elimination.

[1]  Juan Manuel Peña,et al.  Progressive iterative approximation and bases with the fastest convergence rates , 2007, Comput. Aided Geom. Des..

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

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

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

[5]  H. Bao,et al.  Totally positive bases and progressive iteration approximation , 2005 .

[6]  J. Uhlig.  C. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems. (Series in Automatic Computation) XI + 148 S. Englewood Cliffs, N.J. 1967. Prentice-Hall, Inc. Preis geb. 54 s. net , 1972 .

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

[8]  R. Skeel.  Iterative refinement implies numerical stability for Gaussian elimination , 1980 .

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

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

[11]  Cleve B. Moler,et al.  Iterative Refinement in Floating Point , 1967, JACM.

[12]  J. Ortega.  Numerical Analysis: A Second Course , 1974 .

[13]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

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

[15]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[16]  James Hardy Wilkinson,et al.  Error Analysis of Direct Methods of Matrix Inversion , 1961, JACM.

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

[18]  Juan Manuel Peña,et al.  Shape preserving representations for trigonometric polynomial curves , 1997, Comput. Aided Geom. Des..

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