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The conjugate gradient method from different perspectives.
The (preconditioned) conjugate gradient (CG) algorithm by Hestenes and Stiefel is the iterative method of choice for solving linear systems with a real positive definite symmetric matrix. This method can be seen from several perspectives, and each of these perspectives is useful in some context.
In this talk we concentrate on understanding the CG method. We will show, how to efficiently gather information about the system matrix A as well as about the convergence characteristics during the run of the CG method. Finally, we will comment on practical computations, where we have to take into account the influence of finite precision arithmetic.
Note: the talk will be given in Czech.