Solvers

A solver's solve(A, b, x) method computes an estimate of the model ${\bf x}$ for the given operator ${\bf A}$and a known data vector ${\bf b}$. To test Jag's ability to accommodate a wide variety of application-independent solvers, we implemented six solvers:

• Steepest Descent Solver
• Conjugate Gradient Solver (for linear operators)
• Conjugate Gradient Solver with pre-conditioning
• Conjugate Gradient Solver for nonlinear functionals
• Simplex Solver
• Simulated Annealing Solver

The program fragment of the Steepest Decent Solver in the Appendix demonstrates the simple but powerful abstract mathematical formulations that Jag's class hierarchy provides. The solver exclusively contains abstract interface objects and methods. Consequently, such a solver will work with any implementation of those interfaces.

We additionally devised a scheme that allows a programmer to supply his own report and termination methods to an iterative solver. Both methods are executed at the end of each iteration. The report method might print a statement about the state of the estimation and the termination method decides to continue the iteration or not. By supplying a report and termination method, programmer gains tight control over an iterative solver.

Finally, a NormalEquations class permits a programmer to conveniently set up the normal equations ${\bf (A' A) x = A' b}$ for a given minimization problem ${\bf A x = b}$.