In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose...

In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic...

Derivation of the conjugate gradient method Nonlinear conjugate gradient method Biconjugate gradient method Biconjugate gradient stabilized method Elijah Polak...

Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate...

In numerical linear algebra, the conjugate gradient squared method (CGS) is an iterative algorithm for solving systems of linear equations of the form...

In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system A x = b {\displaystyle {\boldsymbol...

biconjugate gradient method is an algorithm to solve systems of linear equations A x = b . {\displaystyle Ax=b.\,} Unlike the conjugate gradient method, this...

residual over the subspace formed. The prototypical method in this class is the conjugate gradient method (CG) which assumes that the system matrix A {\displaystyle...

similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations...

iterates.  This method, and modifications, are globally convergent under mild conditions, and perform competitively with conjugate gradient methods for many...

steepest descent method and the conjugate gradient method, but proximal gradient methods can be used instead. Proximal gradient methods starts by a splitting...

biconjugate gradient method (BiCG) and has faster and smoother convergence than the original BiCG as well as other variants such as the conjugate gradient squared...

Preconditioned Conjugate Gradient Method (LOBPCG), Wiedemann's coordinate recurrence algorithm, and the conjugate gradient method. Krylov subspace methods Distributed...

Isogonal conjugate, in geometry Conjugate gradient method, an algorithm for the numerical solution of particular systems of linear equations Conjugate points...

Nonlinear conjugate gradient method, generalizes the conjugate gradient method to nonlinear optimization Stochastic gradient descent, iterative method for optimizing...

NEWUOA LINCOA Nonlinear conjugate gradient method Levenberg–Marquardt algorithm Broyden–Fletcher–Goldfarb–Shanno or BFGS method Differential evolution...

optimal control. As a pioneer in computer science, he devised the conjugate gradient method, published jointly with Eduard Stiefel. Born in Bricelyn, Minnesota...

unknowns associated with subdomain interfaces is solved by the conjugate gradient method. Suppose we want to solve the Poisson equation − Δ u = f , u |...

iteration Conjugate gradient method (CG) — assumes that the matrix is positive definite Derivation of the conjugate gradient method Nonlinear conjugate gradient...

usually used as though they were not, e.g. GMRES and the conjugate gradient method. For these methods the number of steps needed to obtain the exact solution...

Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally...

necessarily approximate the optimum. One example of the former is conjugate gradient method. The latter is called inexact line search and may be performed...

space iterative methods, such as the conjugate gradient method or GMRES. In overlapping domain decomposition methods, the subdomains overlap by more than...

9} for Newton or quasi-Newton methods and c 2 = 0.1 {\displaystyle c_{2}=0.1} for the nonlinear conjugate gradient method. Inequality i) is known as the...

\mathbf {J_{r}} } . For large systems, an iterative method, such as the conjugate gradient method, may be more efficient. If there is a linear dependence...

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding...

gradient descent methods can move in any direction that the ridge or alley may ascend or descend. Hence, gradient descent or the conjugate gradient method...

preconditioned iterative methods for linear systems include the preconditioned conjugate gradient method, the biconjugate gradient method, and generalized minimal...

iterative methods. Many of these methods are only applicable to certain types of equations, for example the Cholesky factorization and conjugate gradient will...

using multigrid preconditioners in the locally optimal block conjugate gradient method. Electronic Transactions on Numerical Analysis, 15, 38–55, 2003...