CS370 - Numerical Computation

I took this course because there is a chapter in PMPP that covers how floating numbers are represented, which I haven’t really been ready for.

Things to practice:

  • Calculating from (I did from )
  • Eigenvalues (p.203)

Final Exam

The final exam will be cumulative, i.e., covering all the material in the course: floating point, interpolation/splines, ODEs, Fourier, and numerical linear algebra (which includes page rank, LU, norms/conditioning, etc.).

There will be roughly 9 questions, though each question may consist of multiple parts. Approximately 1/3 of them will be on material from before the midterm (FP, Interpolation, ODEs), and 2/3 will be from after the midterm (Fourier, Numerical Linear Algebra).

Course notes sections corresponding to material covered in lectures and which is ‘testable’ for the final exam:

  • All of Chapter 1 (on floating point numbers)
  • In Chapter 2 (on interpolation), everything up to and including Section 2.5
  • All of Chapter 3 (on parametric curves)
  • In Chapter 4 (on differential equations), everything except Sections 4.5 and 4.8
  • In Chapter 5 (on Fourier transforms), everything up to and including 5.10 (Aliasing), plus 5.12 (2D FFT), but not 5.11 or 5.13
  • All of Chapter 6 (on numerical linear algebra)
  • All of Chapter 6 (on pagerank)

Concepts

Chapter 1

Chapter 2

Chapter 3

Chapter 4: Differential Equations

Chapter 5: Discrete Fourier Transforms

Chapter 6: Numerical Linear Algebra

Chapter 7: Google Page Rank

One of the key ideas is truncation error vs. Stability

Chapter 1

Real numbers potentially have infinitely many digits (think or ), but computers have only finite storage and processing speed. Therefore, a computer uses a floating point number system.

These real numbers will only an approximate representation.

see Floating-Point Number System.

Then, we go over Error.

Machine Epsilon.

Lecture 3

  • Teacher talks about catastrophic cancellation error which I don’t understand

You can rewrite the equation.

I need to catch up on the Taylor series example and understand it.

She says that is due to alternating signs causes catastrophic cancellation sometimes.

We then go into Interpolation.

A2