A family of methods with three‐term recursion formulae

A state‐of‐the‐art survey of a family of vector iterative methods with three‐term recursion formulae is presented. The methods can be classified under two broad categories. The Chebyshev semi‐iterative type of methods and the conjugate gradient type of methods. Relationships between the iteration parameters of the methods are established and computational techniques for estimating these parameters are presented. Numerical tests confirm the superiority of the conjugate gradient method for linear problems and the Chebyshev semi‐iterative methods for nonlinear problems.