OCVdM: Optimally conditioned Vandermonde matrices

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By Walter Gautschi

Purdue University

Matlab routines for computing optimally conditioned Vandermonde matrices

Version 1.0 - published on 23 Apr 2014 doi:10.4231/R7TB14TB - cite this Archived on 25 Oct 2016

Licensed under CC0 1.0 Universal

Description

This software source code investigates numerically the extent to which the condition number of such matrices can be reduced, either by row-scaling or by optimal configurations of nodes. In the latter case we find empirically the condition of the optimally conditioned n × n Vandermonde matrix to grow exponentially at a rate slightly less than (1+√2)^n.

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Notes

This dataset contains 29 Matlab codes and 3 data sets:

Matlab:

  • Fig1a.m
  • VdMsc.m
  • sFig1b.m
  • sVdMsc.m
  • plotFig1a.m
  • plotFig1b.m
  • condVp.m
  • sFig2a.m
  • Fig2b.m
  • condVsc.m
  • plotFig2.m
  • fFig2a.m
  • fFig2b.m
  • sVdMsc1.m
  • plotFig3_1.m
  • sVdMsc2.m
  • plotFig3_2.m
  • sVdMsc3.m
  • plotFig3_3.m
  • optcondVp.m
  • condVp.m
  • condVs.m
  • optcondVs.m
  • condV.m
  • optcondV.m
  • plotoptV.m
  • condVl.m
  • optcondVl.m
  • runVdMlsc.m

Data sets:

  • xoptV
  • xoptVs
  • xoptVp

These software files serve as a companion piece to the paper, "Optimally scaled and optimally conditioned Vandermonde and Vandermonde-like matrices", BIT Numerical Mathematics, 2011, Volume 51, Issue 1, pp. 103-125. doi: 10.1007/s10543-010-0293-1

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