Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In this link, the following result is presented without proof:

Let $a, b, c$ be the lower off diagonal, diagonal, and upper off diagonal elements of a tridiagonal matrix. A pivotless LU decomposition exists if $|a_i| + |c_i| < |b_i|$.

I'm trying to convince myself that this is true (so I don't necessarily need a formal proof), but I'm not sure where to start. Or are there better existence criteria for LU decompositions on tridiagonal matrices?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.