Week 04

Pluto notebooks have been updated to the newest julia version 1.11, videos are those recorded for Winter 23/24.

Direct solvers, sparse matrices

• Pluto notebook: pluto/julia, html, pdf

Iterative solvers, LinearSolve.jl

• Pluto notebook: pluto/julia, html, pdf

• LinearSolve.jl:

  • Documentation

  • Sparse solvers

  • Preconditioners

• Literature on iterative methods:

  • Y. Saad: Iterative methods for sparse linear systems

  • R. S. Varga: Geršgorin and His Circles

  • M. Gutknecht A Brief Introduction to Krylov Space Methods for Solving Linear Systems

  • J. Shewchuk Introduction to the Conjugate Gradient Method Without the Agonizing Pain

  • E.Carson, J.Liesen, Z. Strakoš: 70 years of Krylov subspace methods: The journey continues

  • R. S. Varga: Matrix Iterative Analysis