Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. 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 numerically solving partial differential equations or optimization problems.
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- enIn mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. 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 numerically solving partial differential equations or optimization problems.
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- enIn mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. 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 numerically solving partial differential equations or optimization problems. The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it. The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems.
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- Algorithm
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- Conjugate gradient method
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- enConjugate gradient method
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- Algorithm
- Anne Greenbaum
- Arnoldi iteration
- Basis (linear algebra)
- Belief propagation
- Biconjugate gradient method
- Category:Gradient methods
- Category:Numerical linear algebra
- Cholesky decomposition
- Condition number
- Conjugate gradient method
- Conjugate residual method
- Conjugate transpose
- Double integrator
- Double-precision floating-point format
- Eduard Stiefel
- Eigenvalue
- Energy minimization
- Feedback Control
- File:Conjugate gradient illustration.svg
- Gauss–Seidel method
- GNU Octave
- Gradient descent
- Gram–Schmidt process
- Hermitian
- Hessian matrix
- Incomplete Cholesky factorization
- Inner product space
- Iterative method
- Jacobi method
- Krylov subspace
- Lanczos iteration
- Line search
- Magnus Hestenes
- Mathematical optimization
- Mathematics
- MATLAB
- Nonlinear conjugate gradient
- Nonlinear conjugate gradient method
- Normal equations
- Numerical solution
- Octave code
- Optimal control
- Partial differential equation
- Polynomial ring
- Positive-definite matrix
- Preconditioner
- Preconditioning
- Quadratic function
- Real number
- Residual (numerical analysis)
- Rounding errors
- Round-off error
- Sparse matrix
- Sparse matrix–vector multiplication
- Spectrum of a matrix
- Steepest descent
- Symmetric matrix
- System of linear equations
- Transpose
- Z4 (computer)
- SameAs
- 4255670-3
- CG-Verfahren
- Conjugate gradient method
- Er79
- Konjugált gradiens módszer
- m.052fr3
- Méthode du gradient conjugué
- Metoda gradientu sprzężonego
- Metodo del gradiente coniugato
- Método del gradiente conjugado
- Método do gradiente conjugado
- Q1191895
- Метод сопряжённых градиентов (для решения СЛАУ)
- Метод спряженого градієнта
- روش گرادیان مزدوج
- 共役勾配法
- 共轭梯度法
- 켤레기울기법
- SeeAlso
- Preconditioner
- Subject
- Category:Gradient methods
- Category:Numerical linear algebra
- Octave code
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- enConjugate gradients, method of
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