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.

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enIn 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.
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enIn 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.
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Derivation of the conjugate gradient method
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enDerivation of the conjugate gradient method
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Arnoldi iteration
Category:Articles containing proofs
Category:Gradient methods
Category:Numerical linear algebra
Category:Optimization algorithms and methods
Conjugate direction method
Conjugate gradient method
Eigenvalue
Gaussian elimination
Gram-Schmidt orthogonalization
Iterative method
Krylov subspace
Lanczos iteration
LU factorization
Numerical linear algebra
Optimization (mathematics)
Orthonormal
Partial pivoting
Positive-definite matrix
Symmetric matrix
System of linear equations
Upper Hessenberg matrix
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Derivation of the conjugate gradient method
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共轭梯度法的推导
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Category:Articles containing proofs
Category:Gradient methods
Category:Numerical linear algebra
Category:Optimization algorithms and methods
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