Math 5610 Fundamentals of Computational Mathematics: Homework 3 Problems

  1. Task: Implement a method that returns the absolute error in the approximation of one vector by another when the 2-norm is used. Make sure to add an entry to your software manual to document the work.
  2. Task: Implement a method that returns the absolute error in the approximation of one vector by another when the 1-norm is used. Add an entry to your software manual that documents the method.
  3. Task: Implement a method that returns the absolute error in the approximation of one vector by another when the $\infty$-norm is used. Add an entry to your software manual that documents the method.
  4. Task: Implement a method that returns the 1-matrix norm of a given square matrix. Add an entry to your software manual that documents the method.
  5. Task: Implement a method that returns the $\infty$-norm of a given square matrix. Add an entry to your software manual that documents the method.
  6. Task: Implement a method that returns the dot produce of two vectors of the same length. Add an entry to your software manual that documents the method.
  7. Task: Implement a method that returns the cross-product of two vectors of length three. Add an entry to your software manual that documents the method.
  8. Task: Implement a method that returns the product of two matrices with an equal inner dimension. Add an entry to your software manual that documents the method.
  9. Task: Write a routine that will generate a diagonally dominant matrix that has real values in all entries of the matrix. Add an entry to your for the method you create.
  10. Task: Search the internet for sites that define and discuss the Frobenius matrix norm. Also, look for sites that define consistent matrix norms. Summarize in a paragraph or two what you found and as usual cite the sites.