Search results
Results From The WOW.Com Content Network
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.
English: Example of finding the root of the function represented by the red line (cos(x) − x 3) using the secant method, with the increasingly accurate approximations represented by the blue straight lines.
The following is an example of a possible implementation of Newton's method in the Python (version 3.x) programming language for finding a root of a function f which has derivative f_prime. The initial guess will be x 0 = 1 and the function will be f ( x ) = x 2 − 2 so that f ′ ( x ) = 2 x .
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 ...
Broyden suggested using the most recent estimate of the Jacobian matrix, J n−1, and then improving upon it by requiring that the new form is a solution to the most recent secant equation, and that there is minimal modification to J n−1:
This example program, written in the C programming language, is an example of the Illinois algorithm. To find the positive number x where cos( x ) = x 3 , the equation is transformed into a root-finding form f ( x ) = cos( x ) − x 3 = 0 .
As h approaches zero, the slope of the secant line approaches the slope of the tangent line. Therefore, the true derivative of f at x is the limit of the value of the difference quotient as the secant lines get closer and closer to being a tangent line: ′ = (+) ().