Application 3 Table of Contents
Description of Tasks
Task 1
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.
Task 2
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.
Task 3
Implement a method that returns the absolute error in the approximation of one vector by another when the -norm is used. Add an entry to your software manual that documents the method.
Task 4
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.
Task 5
Implement a method that returns the -norm of a given square matrix. Add an entry to your software manual that documents the method.
Task 6
Implement a method that returns the dot product of two vectors of the same length. Add an entry to your software manual that documents the method.
Task 7
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.
Task 8
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.
Task 9
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.
Task 10
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.