Hardware support for floating-point intensive applications like multimedia and graphics processing is rapidly gaining importance. The use of add-on cards for graphics processing, image rendering and 3D acceleration are now common even in home PCs. Recently, reconfigurable systems, in the form of FPGAs, have gained popularity in construction of such specialized hardware. In this work, we take a look at a particular class of applications involving highly computationally-intense iterative floating-point algortithms for solving large sparse linear systems and present a case for achieving improvement in their execution by using a Custom Integrated Circuit. Our design uses novel methods to overcome precision and numerical instability problems that arise in earlier implementations which used FPGAs. Our design consists of an add-on card which contains a custom Reconfigurable Integrated Circuit with multiple processors on a single die. We believe that our system is the first of its kind to use these algorithms for solving large sparse linear systems in real-time. The cost-effectiveness and computational power provided by our system will allow applications like real-time object modeling, fluid flow modeling and animation to be run even on home PCs by using this add-on card.