Matrix Solver: [A]{x}={b}
The NASA General-Purpose equation Solver, GPS, solves large matrix systems whose equations may be sparse or dense, positive definite or indefinite using minimal computer time and memory.

Development
Early research on dense, banded and sparse matrix equation solvers on single and multiprocessor computers led to an extremely fast Vector Sparse Solver, VSS, for structural analysis. VSS was renamed GPS when it was extended to solve complex interface structures (involving indefinite matrices) and Electromagnetic and Acoustic applications (involving complex matrices). GPS solution times for 16,152 to 551,535 equation aircraft models for one SGI processor are now possible on current PCs. Via one customizable makefile, users can maximize GPS performance on their computer with no source code changes.

Significance
The GPS capability to solve indefinite matrices enables integrated analysis. GPS speed and minimal memory requirement has enabled the analysis of complex structural, electromagnetic and acoustic applications with over 8 million complex equations. It has enabled the solution of applications on PCs that formerly required supercomputers. GPS enabled GENOA to speed solutions 10x and solve 10x larger problems resulting in the 1999 NASA Software of the Year Award.

Status/Plans
Feedback from hundreds of GPS "beta" users is helping bring the code to production quality. In addition to its development and use on NASA High-end computers, GPS has been adapted for high-performance workstations and PCs.

Availability
To request the fast FORTRAN version, complete this form. NASA example data sets are provided in the NASA Matrix Format.

Support/User Feedback
GPS Users are encouraged to provide NASA feedback (via email), post questions, answers, comments, describe enhancements and even include (as attachments) any software additions others may benefit from.