The conjugate gradient method

Karl Schleicher
  • The Leading Edge, April 2018, Society of Exploration Geophysicists
  • DOI: 10.1190/tle37040296.1

A tutorial on the conjugate gradient method, a method to solve large linear problems

What is it about?

The conjugate gradient method can be used to solve many large linear geophysical problems like least squares migration and full waveform inversion. This tutorial provides simple code to solve an easily to understood problem to demonstrate the method. The code can easily be adapted to solve a large linear inversion problem.

Why is it important?

The conjugate gradient method is often used to solve large problems because the more familiar linear algebra method like gaussian elimination are much more expensive — that is, even a large computer may not be able to find a useful solution in a reasonable amount of time.


Karl Schleicher (Author)
University of Texas at Austin

I found pseudo code to implement the conjugate gradient method buried in a reflection tomography paper Guo, J., et all, 2002). The pseudo code was a minor point, but I referred back to it several times during my career. I also search repeatedly tracked down other references. I wanted to pull to gather these references for myself and others. I hope it will help others use the conjugate gradient method in their research.

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The following have contributed to this page: Karl Schleicher