MCS 471 Computer Problem 2: Computational Linear Algebra

with Maple OR Octave

Due Monday 31 March 1997



Background Reading: Gerald and Wheatley, Chapter 2

Topics

  1. Forward Gaussian Elimination with Back Substitution
  2. Virtual Row (Partial) Pivoting and Row Scaling
  3. Virtual Full Pivoting
  4. Linear Algebra Computational Complexity
  5. Determinants, Inverse and Multiple RHSs by FGE
  6. LU Decomposition with and without Pivoting
  7. Norms, Condition Numbers and Error Propagation
  8. Multidimensional Newton's Method (Nonlinear Algebra)

Octave/Maple Homework Problems:

You can use either Octave or Maple for this assignment. You must hand in a Octave or Maple worksheet that is well documented with comments. Refer to the Class Octave and Maple Pages, or in particular to the quick help linear algebra pages are suggested:

 


  1. Create a 6×6 random matrix A and a 6×1 random vector B using either Octave or Maple tools.
  2. Solve the linear equation A*X=B for the solution X.
  3. Compute the Residual Vector R. How accurate or how good would you say the solution was according to substitution errors?
  4. Compute the Determinant of A.
  5. Compute the Condition Number in the 1-norm for A.
  6. Using the multidimensional Newton's method, approximate the vector zero,(f,g)=(0,0), when using the starting vector iterate (x,y) = (1., 1.) and finding the three (3) more iterates. How close are the last two (2) vector interates in the 1-norm.



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