# 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 $F_{k}$ from $f_{k}$ (I did $f_{k}$ from $F_{k}$)
- 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

- Initial Value Problem
- Logistic Growth
- Forward Euler Method
- Backward Euler Method
- Stability of Algorithms

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 $π$ or $e$), 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.

#### 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

$ 0101000 0000000 0101000 0110000 0000001 0000100 0000010 $