Solution of finite systems of equations by interval iteration

In actual practice, iteration methods applied to the solution of finite systems of equations yield inconclusive results as to the existence or nonexistence of solutions and the accuracy of any approximate solutions obtained. On the other hand, construction of interval extensions of ordinary iteration operators permits one to carry out interval iteration computationally, with results which can give rigorous guarantees of existence or nonexistence of solutions, and error bounds for approximate solutions. Examples are given of the solution of a nonlinear system of equations and the calculation of eigenvalues and eigenvectors of a matrix by interval iteration. Several ways to obtain lower and upper bounds for eigenvalues are given.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041.