PROGRAMMING ALGEBRA

Fundamentally, the Jag library, as well as its predecessors CLOP and HCL, is designed to find estimates for a Hilbert vector x subject to  

$${\bf A x \approx b},$$ (1)

where ${\bf b}$ is a known vector, and ${\bf A}$ is a linear or nonlinear operator In general, Jag does not assume that A is square, a matrix, or full rank, that the data is consistent, over-determined, or under-determined. Furthermore, Jag does not assume that a solution is unique or that a solution even exists. Jag only requires that the problem is of the form stated in equation 1.

To address the problem ${\bf A x \approx b}$ a programmer needs three basic object types or classes: vector objects that contain the data ${\bf b}$ and the model ${\bf x}$, an operator object that implements the operator ${\bf A}$ and a solver object that, given the vector and operator objects, approximates a solution.