6. A system as in claim 4 , wherein the method of conjugate residuals terminates when the α parameter in the method of conjugate residuals has a value not greater than 0.
4. A system for training a program by optimizing a set of program parameter values, comprising: a first set of computational elements for modeling the program to be trained, the processors receiving an input vector and providing an output vector; a second set of computational elements for optimizing the parameter values using an iterative method, wherein successive updates of the parameter values are provided by a method of conjugate residuals, which computes each of the successive updates by solving a set of linear equations involving a Hessian matrix and a gradient vector; and a control unit for controlling the operations of the first and second sets of computational elements.