In solving large linear systems, it is often attractive to use Cholesky triangularization, followed by forward and backward substitutions. In computational problems such as in the nonlinear finite element method, solution is attained incrementally, with the stiffness matrix slightly modified whenever it is updated. The goal of the present investigation is to introduce and demonstrate an iterative method of determining the changes the triangular factors ensuing from modifying the stiffness matrix. A heuristic convergence argument is given, as well as a simple example indicating rapid converence. Apparently no efficient iterative method for matrix triangularization has previously been established.
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