Sum benchmark

Compute set of real values to be summed with an a priori known sum and specified condition number

Description

For a given n, a condition number cth and a value s, Sumbench.m computes a n-vector x with x(1)+...+x(n) = s exactly and whose the sum condition number is about cth within sharp bounds. The true condition number is also returned.
An option is given to return an x such that the exact sum is not exactly a floating point but whose value is described 2 floating point. In this case a third output argument v is a 2 vector such that s= v(1)+ v(2) with v(2)<eps*v(1) ( no overlap).
Sumbench calls another m file exactsum.m which can be used directly for personnal test purpose. This small routines computes the exact sum of any given n- vector. See the comments for details.

• Acknowledgements: This submission has inspired the following:; XSum
• MATLAB release: MATLAB 7.5 (R2007b)
• Other requirements: nothing, probably run with old matlab version