For positive definite matrices only.
TODO application.
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The HPCG benchmark uses a preconditioned conjugate gradient (PCG) algorithm to measure the performance of HPC platforms with respect to frequently observed but challenging patterns of computing, communication, and memory access. While HPL provides an optimistic performance target for applications, HPCG can be considered as a lower bound on performance. Many of the top 500 supercomputers also provide their HPCG performance as a reference.
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A system of linear equations is a collection of two or more linear equations that involve the same set of variables. The goal is to find the values of these variables that satisfy all the equations in the system simultaneously. Systems of linear equations can be classified based on their number of solutions: 1. **Consistent and Independent**: The system has exactly one solution. The lines represented by the equations intersect at a single point.