numerical-stability

Strategies for debugging numerical stability issues?

Dear SO, I'm trying to write an implementation of Wilson's spectral density factorization algorithm [1] for Python. The algorithm iteratively factorizes a [QxQ] matrix function into its square root (it's sort of an extension of the Newton-Raphson square-root finder for spectral density matrices). The problem is that my implementation o...

positive semi-definite matrices and numerical stability ?

i'm trying to do factor analysis for a co-occurrence matrix(C) , which is computed from the term-document matrix(TD) as follows: C=TD*TD' In theory C should be positive semi-definite , but it isn't and the factor analysis algorithm can't work with it because of this.I can't change the algo because of speed reasons). I look it up and ...

Articles on analysis of mixed precision numerical algorithms?

Hi! Many numerical algorithms tend to run on 32/64bit floating points. However, what if you had access to lower precision (and less power hungry) co-processors? How can then be utilized in numerical algorithms? Does anyone know of good books/articles that address these issues? Thanks! ...

In Python small floats tending to zero

Hey! I couldn't find an answer to this problem so I'm asking it here: I have a Bayesian Classifier programmed in Python, the problem is that when I multiply the features probabilities I get VERY small float values like 2.5e-320 or something like that, and suddenly it turns into 0.0. The 0.0 is obviously of no use to me since I must find...

Good algorithm for calculating ln(1-x) for small (and occasionally large) x

I'm looking for an algorithm to calculate ln(1-x). x is often small (<0.01), but occasionally it might be larger. Algorithm needs to be accurate, and not too slow. I'd rather not use library for ln(x), because I might lose accuracy. ...