# Definition:Conjugate Gradient Method

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## Definition

The **conjugate gradient method** is an iterative technique of solving a system of simultaneous linear equations $\mathbf A \mathbf x = \mathbf b$ in which the matrix of coefficients $\mathbf A$ is symmetric and positive definite.

Its use is particularly appropriate when $\mathbf A$ is sparse, because each iteration involves a single product between the matrix and a vector.

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## Also see

- Results about
**the conjugate gradient method**can be found**here**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**conjugate gradient method** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**conjugate gradient method**