Various expressions of Ax = b, or Gm = d if you prefer, to illustrate linear inversion in geophysical problems.
This is a chrestomathy, sort of. I'm trying to reproduce the same (more or less) workflow in all of the following languages:
The idea is to use the fundamentals of linear algebra (dot products, inverses, etc), rather than high-level functions. But where those high-level solving functions exist, we should mention and illustrate them too.
All of these notebooks can certainly be improved upon: suggestions and pull requests welcome!
This series of notebooks was inspired by Mauricio Sacchi's course notes, which includes MATLAB implementations, and grew from there.
I've found the following resources very helpful.
- Stephen Boyd's notes from his course on linear dynamical systems at Stanford.
- Mauricio Sacchi's notes from his course at the University of Alberta.
- Francis Jones and Doug Oldenberg's intro to linear algebra from their courses at UBC.
- Roel Snieder and Jeannot Trampert's notes entitled Inverse problems in geophysics from Colorado School of Mines.