Derivation of the conjugate gradient method

In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system where is symmetric positive-definite. The conjugate gradient method can be derived from several different perspectives, including specialization of the for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. The intent of this article is to document the important steps in these derivations.

Derivation of the conjugate gradient method

In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system where is symmetric positive-definite. The conjugate gradient method can be derived from several different perspectives, including specialization of the for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. The intent of this article is to document the important steps in these derivations.