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In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method , so it is considered a quasi-Newton method .
Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0.It was first presented by David E. Muller in 1956.. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method.
One class of examples is the staggered geometric progressions that get closer to their limits only every other step or every several steps, for instance the example () =,, /, /, /, /, …, / ⌊ ⌋, … detailed below (where ⌊ ⌋ is the floor function applied to ). The defining Q-linear convergence limits do not exist for this sequence ...
The simplest form of the formula for Steffensen's method occurs when it is used to find a zero of a real function; that is, to find the real value that satisfies () =.Near the solution , the derivative of the function, ′, is supposed to approximately satisfy < ′ <; this condition ensures that is an adequate correction-function for , for finding its own solution, although it is not required ...
So for example, by using the equality = , the equation = can be transformed into =, which allows for the solution to the equation = (where :=) to be used; that solution being: = +, which becomes: = + where using the fact that () = and substituting := proves that another solution to = is: = + + +.
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965. [1]Newton's method for solving f(x) = 0 uses the Jacobian matrix, J, at every iteration.
Quasi-Newton methods are a generalization of the secant method to find the root of the first derivative for multidimensional problems. In multiple dimensions the secant equation is under-determined, and quasi-Newton methods differ in how they constrain the solution, typically by adding a simple low-rank update to the current estimate of the ...
In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form f(x) = 0.The idea is to use quadratic interpolation to approximate the inverse of f.