IEEE Transactions on Automatic Control, Vol.52, No.6, 1014-1026, 2007
A control-theoretic approach to the design of zero finding numerical methods
In this paper, it is shown how'standard iterative methods for solving linear and nonlinear equations can be designed from the point of view of control. Appropriate choices of control Lyapunov functions (CLFs) lead to both continuous and discrete-time versions of the Newton-Raphson and conjugate gradient algorithms as well as new variants.
Keywords:conjugate gradient (CG) algorithm;control Lyapunov functions (CLFs);iterative methods;proportional-integral-derivative control;zero finding methods