Abstract

It is well known that the crucial step in the mathematical modeling of the kidney involves the determination of the roots of large systems of sparse non-linear algebraic equations. We utilize the information about the flow directions and the physiological connectivity of the various tubes in the kidney to develop a sparse matrix version of Newton's method for the solution of these equations. The storage requirement for our method is independent of the number of tubes in the model, and its rate of convergence is that of Newton's method.

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