Search results
Results From The WOW.Com Content Network
The Barzilai-Borwein method [1] is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear trend of the most recent two iterates. This method, and modifications, are globally convergent under mild conditions, [ 2 ] [ 3 ] and perform competitively with conjugate gradient methods ...
It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.
In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction.Its use requires that the objective function is differentiable and that its gradient is known.
By using the dual form of this constraint optimization problem, it can be used to calculate the gradient very fast. A nice property is that the number of computations is independent of the number of parameters for which you want the gradient. The adjoint method is derived from the dual problem [4] and is used e.g. in the Landweber iteration ...
The conjugate gradient method can be applied to an arbitrary n-by-m matrix by applying it to normal equations A T A and right-hand side vector A T b, since A T A is a symmetric positive-semidefinite matrix for any A. The result is conjugate gradient on the normal equations (CGN or CGNR). A T Ax = A T b
The FIRE movement has gained popularity as a goal for people seeking to break free from the traditional retirement age. The standard retirement age is 67 for people born after 1960, but FIRE ...
A system of linear equations = consists of a known matrix and a known vector. To solve the system is to find the value of the unknown vector x {\displaystyle {\mathbf {x}}} . [ 3 ] [ 5 ] A direct method for solving a system of linear equations is to take the inverse of the matrix A {\displaystyle A} , then calculate x = A − 1 b {\displaystyle ...