The conjugate gradient method is an algorithm for numerical resolution of particular systems of linear equations, namely those whose matrix is defined as positive.
The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition.
Large sparse systems often arise when solving partial differential equations or optimization problems numerically.
The conjugate gradient method can also be used to solve unconstrained optimization problems.
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