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I'm working on a project which seems to be encountering a problem.

I took Linear Algebra a few years ago in college, and haven't really applied it very much so I'm at a bit of a loss here.

I have a solution to a iterative nonlinear least squares problem: Trilateration with n distances.

I'm implementing the algorithm found in this PDF in java using the JAMA library.

I don't understand much of the math here, and I need to figure out why my matrices are singular (unfortunately the inverse is part of the equation handed to me).

So I guess I'm asking a few things.

1. For Equation (40) (pg 18) R_{{k+1}}=R_{{k}}-(J^{T}_{{k}}J_{{k}})^{-1}J_{{k}}f

I'm ending up with aJ^{T}_{{k}}J_{{k}}term which is singular. This means I cannot directly solve this equation. But while I'm familiar with solving equations of the formAx=BI'm not really sure how to find an alternate solution for equation (40).

2. How robust is the JAMA library in general, is there a better linear algebra system for java?

Thanks!

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# Understanding Solutions and Singular Matrices

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