Update Methods for Highly Structured Systems of Nonlinear Equations
Jake Avila, Paul Concus · SIAM Journal on Numerical Analysis · 1979
Often it is desirable to incorporate known structure of the Jacobian matrix into numerical algorithms for solving systems of nonlinear equations by Broyden update methods. Here we develop a technique for accomplishing this for a certain highly structured system of equations arising as the discrete form of an eigenvalue problem for a nonlinear elliptic partial differential equation of nuclear reactor analysis. We demonstrate how the technique, which is formulated in terms of a pseudo-inverse, can be extended to incorporate other, more general, structures. As an example, we obtain known minimal update formulas for preserving sparsity and symmetry as special cases of the technique. Numerical results are given for the nonlinear eigenvalue problem.