Search Results for ""

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

A root-finding algorithm based on the iteration formula x_(n+1)=x_n-(f(x_n))/(f^'(x_n)){1+(f(x_n)f^('')(x_n))/(2[f^'(x_n)]^2)}. This method, like Newton's method, has poor ...

A method of determining coefficients alpha_l in an expansion y(x)=y_0(x)+sum_(l=1)^qalpha_ly_l(x) so as to nullify the values of an ordinary differential equation L[y(x)]=0 ...

A method used by Gauss to solve the quadratic Diophantine equation of the form mx^2+ny^2=A (Dickson 2005, pp. 391 and 407).

A method of determining coefficients alpha_k in a power series solution y(x)=y_0(x)+sum_(k=1)^nalpha_ky_k(x) of the ordinary differential equation L^~[y(x)]=0 so that ...

Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions, ...

The method of exhaustion was an integral-like limiting process used by Archimedes to compute the area and volume of two-dimensional lamina and three-dimensional solids.

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...