An Introduction to the Conjugate Gradient Method

Add to your list(s) Download to your calendar using vCal

• Jihao Andeas Lin, University of Cambridge
• Wednesday 13 March 2024, 11:00-12:30
• Cambridge University Engineering Department, CBL Seminar room BE4-38..

If you have a question about this talk, please contact Isaac Reid.

Zoom link available upon request (it is sent out on our mailing list, eng-mlg-rcc [at] lists.cam.ac.uk). Sign up to our mailing list for easier reminders via lists.cam.ac.uk.

(Taken from: An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, Jonathan Richard Shewchuk. Andy will walk us through this article.)

The Conjugate Gradient Method is the most prominent iterative method for solving sparse systems of linear equations. Unfortunately, many textbook treatments of the topic are written with neither illustrations nor intuition, and their victims can be found to this day babbling senselessly in the corners of dusty libraries. For this reason, a deep, geometric understanding of the method has been reserved for the elite brilliant few who have painstakingly decoded the mumblings of their forebears. Nevertheless, the Conjugate Gradient Method is a composite of simple, elegant ideas that almost anyone can understand. Of course, a reader as intelligent as yourself will learn them almost effortlessly.

The idea of quadratic forms is introduced and used to derive the methods of Steepest Descent, Conjugate Directions, and Conjugate Gradients. Eigenvectors are explained and used to examine the convergence of the Jacobi Method, Steepest Descent, and Conjugate Gradients. Other topics include preconditioning and the nonlinear Conjugate Gradient Method. I have taken pains to make this article easy to read. Sixty-six illustrations are provided. Dense prose is avoided. Concepts are explained in several different ways. Most equations are coupled with an intuitive interpretation.

Reading recommendations: https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf

This talk is part of the Machine Learning Reading Group @ CUED series.

This talk is included in these lists:

• All Talks (aka the CURE list)
• Cambridge Centre for Data-Driven Discovery (C2D3)
• Cambridge Forum of Science and Humanities
• Cambridge Language Sciences
• Cambridge University Engineering Department Talks
• Cambridge University Engineering Department, CBL Seminar room BE4-38.
• Cambridge talks
• Centre for Smart Infrastructure & Construction
• Chris Davis' list
• Computational Continuum Mechanics Group Seminars
• Featured lists
• Guy Emerson's list
• Hanchen DaDaDash
• Inference Group Journal Clubs
• Inference Group Summary
• Information Engineering Division seminar list
• Interested Talks
• ML
• Machine Learning Reading Group
• Machine Learning Reading Group @ CUED
• Machine Learning Summary
• Quantum Matter Journal Club
• Required lists for MLG
• School of Technology
• Simon Baker's List
• TQS Journal Clubs
• Trust & Technology Initiative - interesting events
• bld31
• custom
• ndk22's list
• ob366-ai4er
• rp587
• yk373's list

Note that ex-directory lists are not shown.