Convergence properties of most minimization algorithms are analyzed through their application to convex quadratic functions. Such functions can be written in the form of equation (3), where A is a positive-definite matrix. We refer to this convex quadratic function throughout this chapter by . For such a function, the unique global minimum satisfies the linear system Since general functions can be approximated by a quadratic convex function in the neighborhood of their local minima, the convergence properties obtained for convex quadratic functions are usually applied locally to general functions. However, such generalizations do not guarantee good behavior in practice on complex, large-scale functions.