437/537 Homework #4
due at the beginning of class, Thursday, Oct 11, 2006
Problems are from Sauer's book unless problem number starts with "X".
Octave/Matlab
X1. [8pts] Do this Octave/Matlab exercise.
I recommend that you type all the commands in a .m file,
and give the calculation results meaningful names,
such as cd = c*d, etc.
Turn in hard copy of your .m file(s), and of the resulting output
of Octave or Matlab.
2.1
2.1 CP 1 [correct GE and BS code: 6pts, correct usage and answer 2pts]
(Do only the Ex 2c problem) with the coefficient of z in eqn 2 changed to 0.97.
2.3
2.3 Ex 6 [6pts] (Forward & backward errors, emfs, and condition number)
Do case (a) by hand, showing all your work.
I suggest you use Octave as a "calculator" for cases (b), (c), (d),
since it is rather tedious to do it by hand.
Make a table of the results, with rows (a) through (d),
and columns for Xc, FE, ||FE||, rel||FE||, BE, ||BE||, rel||BE||, and emf.
Is the condition number attained as the emf in any of the examples?
2.3 Ex 15 [2pts](LU factorization, monitoring multiplier size)
2.3 CP 3 [5pts](Big systems, emfs and condition numbers.) Just use backslash operator,
not your own (unless you're curious to see how well it does). Use Octave's condition number estimator "cond".
2.4 PA=LU factorization
2.4 Ex 3b [3 pts]