This article continues the series on Variable Projection and explains how rewrite the problem using QR decomposition, rather than the more computationally expensive singular value decomposition (SVD).| geo-ant.github.io
In this article, I explore how to efficiently calculate the covariance matrix of the best fit parameters for global fitting problems that use the variable projection (VarPro) algorithm. It’s a very niche topic, but I do need it for my open source library so I might as well write it down. It might be helpful for people looking to gain a deeper understanding of the math behind VarPro.| Geo’s Notepad
In this article, we’ll derive from scratch the well known formulas –and some not so well known ones– for nonlinear least squares fitting from a Bayesian perspective. We’ll be using only elementary linear algebra and elementary calculus. It turns out, that this is a valuable exercise, because it allows us to clearly state our assumptions about the problem and assign unambigous meaning to all components of the least squares fitting process.| Geo’s Notepad
About three years ago, I announced in my previous article on variable projection, that I would write a follow up about VarPro with multiple right hand sides. This is it. Global fitting with multiple right hand sides is an application where VarPro shines because it can bring significant computational savings. Let’s dive right in.| Geo’s Notepad
Announcing a major update of my article on the variable projection algorithm, which you can find on this blog by following this link. The article now contains all the information you need to implement your own VarPro library in a language of your choice.| Geo’s Notepad