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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- 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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