Full Reading List
I have merged all of the readings into a
single list.
ANNOTATED READING
LIST
The
list:
Key:
Ell = Randy Ellis,
Scientific Computing
Notes
Rec = Gerald
Recktenwald, Numerical Methods with
Matlab
Mol = Cleve Moler,
Numerical Computing with
Matlab
Week
11:
Topics:- Least squares
curve fitting.
Class
31 of Ell is on least squares curve fitting. We will actually cover a bit more
than Ell does, so this week reading Rec will be essential.
Chapter 9 of Rec is
on least squares curve fitting. We will only cover the material up to the end of
section 9.2.2. The salient topics are the line fitting, transformations for
fitting apparently non-linear functions, and least squares fit to a linear
combination of functions. The only method I covered is by using the normal
equations. The method using QR-factorization is numerically more stable, but we
will not be covering this method this
term.
Chapter 5 of Mol
is on least squares curve fitting. The lion's share of this chapter deals with
QR-factorizaton, so it is not relevant for us. However, the first few pages of
the chapter, up to the end of section 5.3 are useful. In particular, since I
have assigned some homework from Mol, you should definitely read these few
pages.
Week
10:
Topics:- Gaussian
Quadrature, Euler's method for solving differential
equations.
The Ell
notes covers Gaussian quadrature very tersely in class 22. Class 23 of Ell is on
Euler's method and cover's the topic more or less in the same way that I did
today.
A more
thorough treatment of Gaussian quadrature is done in Rec, section 11.3, however,
some of it does not pertain to the material I covered this term. In particular
section 11.3.4 on computing the nodes and weights can be skipped. You will need
to read section 11.3.5 on composite Gaussian quadrature (also known as Gauss
Legendre quadrature) to do one of the homework questions. I will go over this
with you when we do the solutions to the homework next week. Rec. chapter 12
section 12.1 and 12.2 deal with numerical integration of differential equations
and Euler's method. You may want to read the Summary at the end of chapter 12 to
get an idea of some of the other algorithms that are used.
Mol is silent on the
subject of Gaussian quadrature. As for Euler's method section 7.4 describes it
as well as some other so called single step methods. However, most of the rest
of Mol chapter 7 is beyond the scope of this
course.
Week
9:
Topics:- Numerical
quadrature
Ell covers
this topic in classes 19,20, and 21.
In Rec chapter 11 is
on numerical quadrature. You should read the whole chapter, but can skip over
section 11.3 on Gaussian quadrature for now. We will cover that next
week.
Chapter 6 of
Moler is about quadrature.
Week
8: No readings.
Week
7:
Topics:- Piece-wise
polynomial
interpolation.
Ell
covers piece-wise polynomial interpolation in classes 15 and 16. There is no
mention in Ell, of solving the spline coefficients using a tri-diagonal matrix.
I will use the Ell
presentation with the intent that it may be easier to
understand.
Rec covers
Hermite and cubic spline interpolation interpolation in Chapter 10 sections 10.3
Section 10.4 discusses the built in Matlab interpolation routines.
Mol covers Hermite
interpolation in section 3.3 and cubic splines in section 3.5. The interpgui
Matlab m-file is discussed in section
3.7.
Week
6:
Topics:- Polynomial
interpolation using the monomial, Lagrange, and Newton
Bases.
Note: I only
began describing the Newton basis in the last few minutes of Monday's lecture. I
will continue with the Newton Basis next week.
Ell covers polynomial
interpolation in classes 9, 10, and 11. There is no mention in Ell, of using
Vandermonde matrices to interpolate with the monomial basis.
Rec covers the three
methods of interpolation in Chapter 10 sections 10.1 and 10.2.
Mol only talks about
the monomial basis and the Lagrange basis in section 3.1.
Week
5:
Topics:- Norms and
condition
numbers.
Class 28 of
Ell covers norms and condition numbers. The treatment in Ell is somewhat
different than what we did. In particular I did not cover the Frobenius norm.
Furthermore, I did not discuss using Eigevalues for computing the Matrix 2-norm.
In passing Class 29 of Ell discusses LU decomposition, strictly speaking LU
decomposition is last weeks
topic.
Vector and
matrix norms are covered in Rec sections 7.1.2 and 7.2.4 respectively. Section
8.3 of Rec discusses conditioning and the effects of small perturbations on
ill-conditioned systems. My lectures this week follow the presentation in
Rec.
As usual Mol uses
the fewest words to cover a topic, and you can find his treatment of norms and
condition numbers in section 2.9.
Week
4:
Topic:- Gaussian
Elimination, LU decomposition, and
pivoting.
Class 26 in
Ell is on Gaussian elimination, and class 27 is on pivoting. There is all that
Ell does on this topic. We have done and will do considerably
more.
Chapter 7 in Rec
is a review of linear algebra. This week you should read section 7.1 , 7.2
(7.2.4 vector norms will be on next weeks reading list and I will discuss it in
class, so you can skip 7.2.4 for now.) 7.3.4, 7.3.5, 7.4.1, 7.4.2, 7.4.3.
Most of this should be a
review of the linear algebra you have already taken. I will not be actively
lecturing on these topics, rather the expectation is that you can brush up on
this material on your
own.
Chapter 8 in Rec
covers Gaussian elimination and LU decomposition. This week read 8.1 8.2 and
8.4.1
Chapter 2 in Mol
sections 2.1 - 2.7 covers what I have done this week in the fewest number of
words.
Week
3:
Topic:- Taylor
series.
Taylor series
are covered in Ell Class
1.
Taylor series are
discussed in connection to truncation error in Rec Section
5.3.
Week
2:
Topics: - Root finding
algorithms, Matlab
programming
Root
finding algorithms relevant to this class are covered in Ell Classes 5 and 6.
Root finding algorithms
relevant to this class are covered in Rec chapter 6 sections up to the end of
section 6.6.
Root finding
algorithms are covered in Mol chapter 4.
Note: I won't hold
you responsible for the material on Inverse Quadratic Interpolation. We may get
back to this when we cover interpolation
algorithms.
For a
general introduction to Matlab Part I of Rec is good. For HW-3 chapter 3 is
particularly
useful.
Week
1:
Topics: - Matlab Intro -
floating point
numbers
The Matlab
example done in lecture 1 is taken from Mol section
1.1
The material on magic
squares from Hmwk 1 is in Mol section
1.4
For a general
introduction to Matlab Part I of Rec is good. For Hmwk 1 chapter 2 is
particularly
useful.
Floating point
numbers are covered in Ell Classes 2 and
3.
Floating point numbers
are covered in sections 5.1 and 5.2 of Rec.
Floating point numbers are
covered in Mol section
1.7.
My class notes
are a distillation of all 3 presentations leaving some things out and adding
other things in.
Posted: Fri - December
2, 2005 at 11:44 AM