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If most problems you encounter are numerical in nature,
there is a good chance that you are reading the wrong book.
Numerical Recipes [PFTV86]
gives a terrific overview to the fundamental
problems in numerical computing, including linear algebra, numerical
integration, statistics, and differential equations.
Different flavors of the book include source code for all the algorithms in
C, Pascal, and Fortran.
Their coverage is skimpier on the combinatorial/numerical problems
we consider in this section, but you should be aware of that book.
Numerical algorithms tend to be different beasts than combinatorial
algorithms, for at least two distinct reasons:

Issues of Precision and Error 
Numerical algorithms typically perform repeated
floatingpoint computations,
which accumulate error at each operation until, eventually, the results
are meaningless.
An amusing example [SK93] concerns the Vancouver Stock Exchange,
which over a twentytwo month period accumulated sufficient roundoff error
to reduce its index from the correct value of 1098.982 to 574.081.
A simple and dependable way to test for roundoff errors in numerical
programs is to run them both at single and double precision, and then
think hard whenever there is a disagreement.

Extensive Libraries of Codes 
Large, highquality libraries of numerical routines have existed since
the 1960s, which is still not the case for combinatorial algorithms.
This is true for several reasons, including (1) the early emergence of
Fortran as a standard for numerical computation, (2) the nature of
numerical computations to remain independent
rather than be embedded within large applications, and (3)
the existence of large scientific communities needing general
numerical libraries.
Regardless of why, you should exploit this software base.
There is probably no reason to implement algorithms
for any of the problems in this section instead of stealing existing codes.
Searching Netlib (see Section ) is always a good
place to start.
Most scientist's and engineer's ideas about algorithms derive
from Fortran programming and numerical
methods, while computer scientists grew up programming with pointers and
recursion, and so are comfortable with the more sophisticated
data structures required for combinatorial algorithms.
Both sides can and should learn from each other,
since several problems
such as pattern recognition can be modeled either numerically
or combinatorially.
There is a vast literature on numerical algorithms.
In addition to Numerical Recipes, recommended books include:

Skeel and Keiper [SK93] 
A readable and interesting treatment of basic numerical methods,
avoiding overly detailed algorithm descriptions through its use of the
computer algebra system Mathematica.
I like it.

Pizer and Wallace [PW83] 
A numerical analysis book written for computer scientists, not engineers.
The organization is by issues instead of problems.
A different but interesting perspective.

Cheney and Kincaid [CK80] 
A traditional Fortranbased numerical analysis text, with discussions of
optimization and Monte Carlo methods in addition to such standard topics
as rootfinding, numerical integration, linear systems, splines,
and differential equations.

Buchanan and Turner [BT92] 
Thorough languageindependent treatment of all standard topics,
including parallel algorithms.
Most comprehensive of the texts described here.
Next: Solving Linear Equations
Up: A Catalog of Algorithmic
Previous: KdTrees
Algorithms
Mon Jun 2 23:33:50 EDT 1997