Conjugate gradient methods: Difference between revisions
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== Introduction == | == Introduction == | ||
The conjugate gradient method (CG) was originally invented to minimize a quadratic function:<br> | The conjugate gradient method (CG) was originally invented to minimize a quadratic function:<br> | ||
<math>F(\textbf{x})=\frac{1}{2}\textbf{x}^{T}\textbf{A}\textbf{x}-\textbf{b}\textbf{x}</math> | <math>F(\textbf{x})=\frac{1}{2}\textbf{x}^{T}\textbf{A}\textbf{x}-\textbf{b}\textbf{x}</math><br> | ||
where A is an n × n symmetric positive definite matrix, x and b are n × 1 vectors. The solution to the minimization problem is equivalent to solving the linear system, i.e. determining x when ∇F(x) = 0 <br> | |||
<math>\textbf{A}\textbf{x}-\textbf{b} = \textbf{0}</math> | |||
== Theory == | == Theory == | ||
Revision as of 00:50, 28 November 2021
Author: Alexandra Roberts, Anye Shi, Yue Sun (SYSEN6800 Fall 2021)
Introduction
The conjugate gradient method (CG) was originally invented to minimize a quadratic function:
where A is an n × n symmetric positive definite matrix, x and b are n × 1 vectors. The solution to the minimization problem is equivalent to solving the linear system, i.e. determining x when ∇F(x) = 0
