Iterative Methods for Linear and Nonlinear Equations: Matlab Codes

• Linear Equations
  • pcgsol.m : Preconditioned CG
  • gmresb.m : Brute force GMRES
  • gmres.m : GMRES
    Requires givapp.m .
  • bicgstab.m : Bi-CGSTAB
  • tfqmr.m : TFQMR
  • Finite difference solvers for use in Newton iterative method code nsola.m
    • fdkrylov.m , driver for gmres, Bi-CGSTAB, and TFQMR solvers.
    • fdgmres.m , fdtfqmr.m : solvers called by fdkrylov.m .
    • fdkrylov.m also requires dirder.m and givapp.m
• Nonlinear Equations
  • nsol.m : Basic Newton-Shamanskii solver, difference Jacobian, LU factorization.
    Requires the finite-difference Jacobian, diffjac.m , and directional derivative, dirder.m , codes.
  • brsol.m : Locally convergent Broyden solver
  • nsolgm.m : Newton-GMRES solver.
    Requires dirder.m , fdgmres.m , and givapp.m .
  • nsola.m : Newton-Krylov-Armijo code.
    Requires dirder.m , fdgmres.m , fdcgstab.m , fdtfqmr.m , fdkrylov.m , givapp.m , and parab3p.m .
  • brsola.m : Broyden-Armijo code.
• Miscellaneous
  • givapp.m : applies sequence of Givens rotations. Used in gmres.m and fdgmres.m .
  • fish2d.m : Fast Poisson solver, unit square, homogeneous Dirichlet BC.
    Requires sine transform, sintv.m , and inverse sine transform, isintv.m .
  • parab3p.m : Apply three-point safeguarded parabolic model for a line search.