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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.
A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of successive approximation.
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method.SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
Data-flow analysis is a technique for gathering information about the possible set of values calculated at various points in a computer program.A program's control-flow graph (CFG) is used to determine those parts of a program to which a particular value assigned to a variable might propagate.
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an Hermitian matrix, where is often but not necessarily much smaller than . [1]
Since the secant method can carry out twice as many steps in the same time as Steffensen's method, [b] in practical use the secant method actually converges faster than Steffensen's method, when both algorithms succeed: The secant method achieves a factor of about (1.6) 2 ≈ 2.6 times as many digits for every two steps (two function ...
Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a common use and a well-known example.
It implicitly calls the IntoIterator::into_iter method on the expression, and uses the resulting value, which must implement the Iterator trait. If the expression is itself an iterator, it is used directly by the for loop through an implementation of IntoIterator for all Iterator s that returns the iterator unchanged.