Filter Near-Zero Matrix Elements: Reasonable?

[Mr Peanut]

Given A(m,n), eps = Machine Epsilon, fNorm = FrobeniusNorm(A), p >= 1

To filter noise near zero created by floating point error:

if (|Aij| < fNorm * eps *p)
Aij =0
end if

Seem reasonable?

 

[AlephZero]

it's not reasonable, unless you know something more about where the "floating point errors" came from.

In some circumstances a matrix like $\begin{pmatrix}10^{100} & 10^{-100} \\ 0 & 2 \times 10^{100} \end{pmatrix}$ may be perfectly "well behaved", and the small off-diagonal term might be important.

A good (advanced) reference is some of the papers in http://www.netlib.org/lapack/lawns/