There is no one book that covers the bulk of the class material. I will provide lecture notes for most of the lectures. For each lecture a student will be assigned to write up class notes and these notes will be posted on the web page.

Author="Louis A. Hageman and David M. Young",
Title="Applied Iterative Methods",
Publisher="Academic Press, Inc",
Address="San Diego and London",
Series="Computer Science and Applied Mathematics",
Note="Try Google Books"}

Saad's book is out of print but you can get a electronic copy from him.

Author="Yousef Saad",
Title="Iterative Methods for Sparse Linearsystems",
Publisher="PWS Publishing Company",
Series="The PWS Series in Computer Science",

author = "Peter G. Doyle and J. Laurie Snell" ,
title = "Random Walks and Electric Networks" ,
publisher= "Mathematical Association of America" ,
series = "Carus Mathematical Monographs" ,
volume = "22" ,
year = "1984" ,
bibdate = "Tue Oct 12 09:30:43 1993"}

author = {Gene H. Golub and Van Loan, Charles F.},
title = {Matrix Computations},
publisher = {Johns Hopkins University Press},
year = {1996},
edition = {3},

author = {Lloyd N. Trefethen and David Bau},
title = {Numerical Linear Algebra},
publisher = {{SIAM} Press},
year = {1997},

author = {James W. Demmel},
title = {Applied Numerical Linear Algebra},
publisher = {{SIAM} Press},
year = {1997},

author = {F. R. K. Chung},
title = {Spectral graph theory},
publisher = {Amer. Math. Soc},
year = {1997},
number = {92},
series = {Regional Conference Series in Mathematics},
address = {Providence},

author = {James Hardy Wilkinson},
title = {The Algebraic Eigenvalue Problem},
publisher = {Clarendon Press},
year = {1965},
series = {Monographs on Numerical Analysis},
address = {Oxford},

author = {C. Godsil and G. Royle},
title = {Algebraic Graph Theory},
publisher = {Springer},
year = {2001},
volume = {207},
series = {Graduate Text in Mathematics},
address = {New York},

Here is a list of a some very good books covering more classic algorithm design.

Algorithm Design
Kleinberg and Tardos
Addison-Wesley, 2005

Randomized Algorithms
Motwani and Raghavan
Cambridge University Press, 1995

Introduction to Algorithms
T. Cormen, C. Leiserson, R. Rivest, C. Stein
McGraw Hill, 2001

Computer Algorithms, Introduction to Design and Analysis
Sarah Baase, Allen van Gelder
Addison-Wesley, 2000

Introduction to Algorithms: A Creative Approach
U. Manber
Addison-Wesley, 1990

The Design and Analysis of Computer Algorithms
A. Aho, J. Hopcroft, J. Ullman
Addison-Wesley, 1974

Algorithmics: Theory and Practice
G. Brassard, P. Bratley
Prentice Hall, 1996

Computational Geometry
Mark de Berg, Marc van Kreveld, Mark Overmars and Otfried Schwarzkopf
Springer-Verlag, Berlin, 2000