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5.2 Curve Fitting and Interpolation<br />
139<br />
If you know which factorization to use, then all you need to know here is the<br />
syntax of the corresponding function. If you do not know where and how these<br />
factorizations are used, then this is not the right place to learn it; look into your<br />
favorite books on linear algebra. 2<br />
5.1.5 Advanced topics<br />
<strong>MATLAB</strong>'s main strength is its awesome suite of linear algebra functions. There<br />
are hundreds of functions that aid in finding solutions to linear algebra problems,<br />
from very basic problems to very advanced ones. For example, there are more than<br />
10 eigenvalue-related functions. Type lookfor eigenvalue to see a list of these<br />
functions. Among these functions, eigs deserves special mention. This function<br />
was added in <strong>MATLAB</strong> 5 to help find just a few eigenvalues and eigenvectors, a<br />
requirement that frequently arises in large-scale problems.<br />
There is a separate suite of functions for sparse matrices and computations with<br />
these matrices. These functions include<br />
Fo r on-line help<br />
type:<br />
help sparfun<br />
Category<br />
Elementary matrix functions<br />
FUll to sparse conversion<br />
Utility functions<br />
Reordering algorithm<br />
Linear algebra<br />
Linear equations<br />
Example functions<br />
speye , sprand, spdiags<br />
sparse, full, spconvert<br />
nnz , nzmax , spalloc, spy<br />
colamd , colperm , symamd , symrcm<br />
eigs , svds , luinc , choline<br />
peg, bicg , cgs , qmr<br />
Please see the on-line help with help sparfun for a list of these functions and their<br />
brief descriptions. Detailed on-line help is available on each function.<br />
<strong>MATLAB</strong> also provides several functions for operations on graphs or trees, such<br />
as treelayout, treeplot, etree, etreeplot, gplot, etc. These functions are listed<br />
under the sparfun category.<br />
5.2 Curve Fitting and Interpolation<br />
5.2.1 Polynomial curve fitting on the fly<br />
Curve fitting is a technique of finding an algebraic relationship that "best" (in a least<br />
squares sense) fits a given set of data. Unfortunately, there is no magical function<br />
(in <strong>MATLAB</strong> or otherwise) that can give you this relationship if you simply supply<br />
the data. You have to have an idea of what kind of relationship might exist between<br />
the input data (xi) and the output data (yi)· However, if you do not have a firm idea<br />
but you have data that you trust, <strong>MATLAB</strong> can help you explore the best possible<br />
fit. <strong>MATLAB</strong> includes Basic Fitting in itH figure window's Tools menu that lets<br />
you fit a polynomial curve (up to the tenth order) to your data on the fly. It also<br />
2Some of my favorites: Linear Algebra and Its Applications <strong>by</strong> Strang, Saunders HBJ College<br />
Publishers; Matrix Computations <strong>by</strong> Golub and Van Loan, The Johns Hopkins University Press;<br />
Matrix Analysis <strong>by</strong> Horn and Johnson, Cambridge University Press.
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