Conjugate Gradient Method: Solving Linear Systems

This lecture covers the Conjugate Gradient (CG) method for solving linear systems Ax = b without pre-conditioning. The method generates a solution xk at iteration k using pk as the conjugate vector and ak as the step length. The residual rk is also discussed, along with the practical enforcement of conjugation between pk iterations. The lecture further explores parallel and high-performance computing, including MPI and CUDA implementations for dense or sparse matrices. Students are tasked with providing parallel versions of the CG code, profiling the sequential code, and predicting the sequential fraction to apply Amdhal's and Gustafson's laws for evaluation.