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

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

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

gradient descent Coordinate descent Frank–Wolfe algorithm Landweber iteration Random coordinate descent Conjugate gradient method Derivation of the conjugate...

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

The theory of stationary iterative methods was solidly established with the work of D.M. Young starting in the 1950s. The conjugate gradient method was...

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

competitively with conjugate gradient methods for many problems. Not depending on the objective itself, it can also solve some systems of linear and non-linear...

other variants such as the conjugate gradient squared method (CGS). It is a Krylov subspace method. Unlike the original BiCG method, it doesn't require multiplication...

the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does...

in that case the techniques of linear programming are applicable. Adjoint equation Newton's method Steepest descent Conjugate gradient Sequential quadratic...

Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e...

Polyak, subgradient–projection methods are similar to conjugate–gradient methods. Bundle method of descent: An iterative method for small–medium-sized problems...

gradient estimation method commonly used for training neural networks to compute the network parameter updates. It is an efficient application of the...

Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies...

better, the QR factorization of J r {\displaystyle \mathbf {J_{r}} } . For large systems, an iterative method, such as the conjugate gradient method, may...

that the standard conjugate gradient (CG) iterative methods can still be used. Such imposed SPD constraints may complicate the construction of the preconditioner...

Bisection method Euler method Fast inverse square root Fisher scoring Gradient descent Integer square root Kantorovich theorem Laguerre's method Methods of computing...

algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested...

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

Method Scaling, Part II: Gradient Separations". LCGC North America. 32 (3): 188–193. Martin, A. J. P.; Synge, R. L. M. (1941-12-01). "A new form of chromatogram...

Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric...

inverting the matrix.) In addition, L {\displaystyle L} is symmetric and positive definite, so a technique such as the conjugate gradient method is favored...

to the unconstrained case, often via the use of a penalty method. However, search steps taken by the unconstrained method may be unacceptable for the constrained...

parameters, the steepest descent iterations, with shift-cutting, follow a slow, zig-zag trajectory towards the minimum. Conjugate gradient search. This...

between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current...

priors are used. Via numerical optimization such as the conjugate gradient method or Newton's method. This usually requires first or second derivatives...

to try to minimize the forces and this could in theory be any method such as gradient descent, conjugate gradient or Newton's method, but in practice,...

and Rubin. Other methods exist to find maximum likelihood estimates, such as gradient descent, conjugate gradient, or variants of the Gauss–Newton algorithm...

converge to one of them. If the only extremum on the interval is on a boundary of the interval, it will converge to that boundary point. The method operates...