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The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...

An implicit method for solving an ordinary differential equation that uses f(x_n,y_n) in y_(n+1). In the case of a heat equation, for example, this means that a linear system ...

An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

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 ...

A method for solving ordinary differential equations using the formula y_(n+1)=y_n+hf(x_n,y_n), which advances a solution from x_n to x_(n+1)=x_n+h. Note that the method ...

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 ...

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

The Gauss-Seidel method (called Seidel's method by Jeffreys and Jeffreys 1988, p. 305) is a technique for solving the n equations of the linear system of equations Ax=b one ...

The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...