Module 7 Summary

Thomas J. Kennedy

Contents:
1 Objectives
2 Questions to Consider

1 Objectives

Having completed this module students are now prepared to:

  1. Explain the differences between the Riemann Integral and Riemann-Stieltjes Integral.
  2. Apply the weighted L2-Norm, properties of inner products, derivatives, and integrals to explain derivations of Least Squares Approximation.
  3. Explain the impact of basis functions.
  4. Manually (i.e., by hand on paper) build a solution for continuous functions/data.
  5. Discuss the motivation for a single Least Squares notation to reconcile the discrete and continuous cases.

2 Questions to Consider

  1. Why do we need Least Squares approximation?
  2. What does the weighted L2-Norm represent?
  3. What is the key difference between the Riemann Integral and Riemann-Stieltjes Integral?
  4. For the continuous case, why do we sometimes need a different function?
  5. What programs use Least Squares Approximation?
  6. Where did you use Least Squares Approximation, before this course?
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