Bounded Wegstein convergence method

Thus, weights q and 1 — q are applied, respectively, to x and/(jc ). Equation (4.10), withq defined by the slope, is usually employed when the slope is less than 1, such that q < 0. Typically, q is bounded between —20 and 0 to ensure stability and a reasonable rate of convergence. Wegstein s method reduces to the method of successive substitutions, x = / x ), when = 0. 

Thus, Equation 13.36 can be used to accelerate the convergence and is known as the Wegstein method11. If q = 0 in Equation 13.36, the method becomes direct substitution. If q < 0, acceleration of the solution occurs. Bounds are normally set for the value of q to prevent unstable behavior. 

The parameter q may be bounded or modified for better convergence control. Wegstein is the default method in many simulators. 

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