Physics 410: Linear Systems

• Most of the source code covered in class can be found on the phy410 account on the lnx machines lnx in ~phys410/linsys/ex1, ... (organized by lecture).
• General References
  • Numerical Recipes, Chapter 2
  • LAPACK User's Guide (html)
  • LAPACK Source Code (browse directory)
  • BLAS LAPACK Source Code (browse directory)
• Combined handouts (PDF) for the following lectures (does NOT include Maple Worksheet (Lectures 1 & 2) or Solving General Linear Banded Systems notes (Lecture 3)).
• Lecture 1 
  • dgesv.f: LAPACK driver routine for solving general linear system via LU decomposition with partial pivoting.
  • tdgesv.f: Test program illustrating use of dgesv.
    Makefile and output on lnx1. Output on physics.
  • Maple worksheet (PDF) which verifies above test.
• Lecture 2
  • dgtsv.f: LAPACK driver routine for solving general tridiagonal system with partial pivoting.
  • bvp1d.f: Test program illustrating use of dgtsv to solve a 1d boundary-value problem using second-order finite-difference techniques. Makefile and sample output on lnx1. Plots showing level-8 solution and error for levels 5, 6 and 7. Gnuplot "scripts" gpsoln8 and gperr, for making solution and error plots.
• Lecture 3
  • Handout: Solving General Banded Linear Systems (PDF). Lecture version: (PDF).
  • dgbsv.f: LAPACK driver routine for solving general banded system via LU decomposition with partial pivoting.
  • bvp1d4.f: Test program illustrating use of dgbsv to solve a 1d boundary-value problem using mixed second and fourth order finite-difference techniques. Makefile and sample output on lnx1. Plots showing level-4 solution and error for levels 4, 5 and 6.