Least-square inversion with inexact adjoints. Method of conjugate directions: A tutorial |

Method of conjugate directions: A tutorial

**Sergey Fomel**

This tutorial describes the classic method of conjugate directions:
the generalization of the conjugate-gradient method in iterative
least-square inversion. I derive the algebraic equations of the
conjugate-direction method from general optimization principles. The
derivation explains the ``magic'' properties of conjugate gradients.
It also justifies the use of conjugate directions in cases when
these properties are distorted either by computational errors or by
inexact adjoint operators. The extra cost comes from storing a
larger number of previous search directions in the computer memory.
A simple program and two examples illustrate the method.

- Introduction
- IN SEARCH OF THE MINIMUM
- IN SEARCH OF THE DIRECTION

- ALGORITHM
- WHAT ARE ADJOINTS FOR? THE METHOD OF CONJUGATE GRADIENTS

- PROGRAM
- EXAMPLES

- Conclusions
- Bibliography
- About this document ...

2013-03-03