The goal of this toolbox is to provide a collection of
test matrices.
Some of these matrices appears in specific applied mathematics
problems.
For example, the Van Der Monde matrix appears in polynomial interpolation.
Another example is the Hilbert matrix, which arises in the least squares
approximation of arbitrary functions by polynomials.
These test matrices can also be used to experiment with linear algebra
algorithms, such as the resolution of systems of linear equations
or the eigenvalue problem.
For some of these test matrices, the exact eigenvalues, condition number or
invert
is known.
For example, the Hilbert matrix is symetric positive definite.
Another example is Frank's matrix, which has a unit derminant, but
is ill-conditionned.
Features
--------
* makematrix_border : Returns the Border matrix
* makematrix_frank : Returns the Frank matrix, or its reflection about the
anti-diagonal
* makematrix_gallery : Returns the Wilson matrix
* makematrix_wilkinsonm : Returns the Wilkinson - matrix
Functions now provided by Scilab
--------------------------------
The following functions have been removed, as Scilab now provides them:
* makematrix_cauchy(x, y) : gallery("cauchy", x, y)
(a scalar x is interpreted as 1:x by gallery)
* makematrix_circul(x) : gallery("circul", x)
* makematrix_diagonali(n) : diag(1:n)
* makematrix_dingdong(n) : gallery("ris", n)
* makematrix_frankmin(n) : gallery("minij", n)
* makematrix_gallery("cauchy", x [, y]) : gallery("cauchy",
x [, y])
* makematrix_gallery("circul", x) : gallery("circul", x)
* makematrix_gallery(3), makematrix_gallery(5) : gallery(3), gallery(5)
* makematrix_gallery(8) : rosser()
* makematrix_hadamard(n) : hadamard(n)
* makematrix_hankel(n, x) : hankel(x(1:n), x(n:$))
* makematrix_hilbert(n) : hilbm(n)
* makematrix_invhilbert(n) : invhilb(n)
* makematrix_magic(n) : magic(n)
* makematrix_moler(n) : gallery("moler", n)
* makematrix_normal(n) : grand(n, n, "nor", 0, 1)
* makematrix_pascal(n) : pascal(n)
* makematrix_pascal(n, 1) : abs(pascal(n, 1))
* makematrix_pascal(n, -1) : abs(pascal(n, 1))'
* makematrix_rosser() : rosser()
* makematrix_toeplitz(x) : toeplitz(x)
* makematrix_vandermonde(x [, n]) : vander(x [, n])
* makematrix_wilkinsonp(n) : wilkinson(n), for odd n
Demos
-----
* Vandermonde : Interpolation
* Hilbert : Least Squares
* Backslash Test
