Broyden Solver

You are now ready to use a better algorithm to speed your code by an order of magnitude! Implementing the new algorithm requires attention to detail, but is well worth it in the end.

Programming strategy: We are also now at a stage in our software project where our programming strategy must change. This is because our software (Appendix A) is now fully functional, albeit not optimized. Rather than building up the working pieces one at a time and carefully verifying each one, we now can make incremental changes and rerun the code with each change to make sure that it continues to function properly. For the exercises below, please begin with the main program in Appendix A and make the appropriate modifications to it, calling the new program ``test_it''.

• Bookkeeping
  • Debugging
• Improved initial guess
• ``broyden''
  • Matrix G and vector u
    • Declarations:
    • Residual vector :
    • Formation:
  • Solution of G b = u
  • Formation of final Rho[it+1]
• Convergence rate