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GALLERY Higham test matrices.
[out1,out2,...] = GALLERY(matname, param1, param2, ...)
takes matname, a string that is the name of a matrix family, and
the family's input parameters. See the listing below for available
matrix families. Most of the functions take an input argument
that specifies the order of the matrix, and unless otherwise
stated, return a single output.
For additional information, type "help private/matname", where matname
is the name of the matrix family.
cauchy Cauchy matrix.
chebspec Chebyshev spectral differentiation matrix.
chebvand Vandermonde-like matrix for the Chebyshev polynomials.
chow Chow matrix -- a singular Toeplitz lower Hessenberg matrix.
circul Circulant matrix.
clement Clement matrix -- tridiagonal with zero diagonal entries.
compar Comparison matrices.
condex Counter-examples to matrix condition number estimators.
cycol Matrix whose columns repeat cyclically.
dorr Dorr matrix -- diagonally dominant, ill-conditioned, tridiagonal.
(One or three output arguments, sparse)
dramadah Matrix of ones and zeroes whose inverse has large integer entries.
fiedler Fiedler matrix -- symmetric.
forsythe Forsythe matrix -- a perturbed Jordan block.
frank Frank matrix -- ill-conditioned eigenvalues.
gearmat Gear matrix.
grcar Grcar matrix -- a Toeplitz matrix with sensitive eigenvalues.
hanowa Matrix whose eigenvalues lie on a vertical line in the complex
plane.
house Householder matrix. (Three output arguments)
invhess Inverse of an upper Hessenberg matrix.
invol Involutory matrix.
ipjfact Hankel matrix with factorial elements. (Two output arguments)
jordbloc Jordan block matrix.
kahan Kahan matrix -- upper trapezoidal.
kms Kac-Murdock-Szego Toeplitz matrix.
krylov Krylov matrix.
lauchli Lauchli matrix -- rectangular.
lehmer Lehmer matrix -- symmetric positive definite.
leslie Leslie matrix.
lesp Tridiagonal matrix with real, sensitive eigenvalues.
lotkin Lotkin matrix.
minij Symmetric positive definite matrix MIN(i,j).
moler Moler matrix -- symmetric positive definite.
neumann Singular matrix from the discrete Neumann problem (sparse).
orthog Orthogonal and nearly orthogonal matrices.
parter Parter matrix -- a Toeplitz matrix with singular values near PI.
pei Pei matrix.
poisson Block tridiagonal matrix from Poisson's equation (sparse).
prolate Prolate matrix -- symmetric, ill-conditioned Toeplitz matrix.
randcolu Random matrix with normalized cols and specified singular values.
randcorr Random correlation matrix with specified eigenvalues.
randhess Random, orthogonal upper Hessenberg matrix.
randjorth Random J-orthogonal matrix.
rando Random matrix with elements -1, 0 or 1.
randsvd Random matrix with pre-assigned singular values and specified
bandwidth.
redheff Matrix of 0s and 1s of Redheffer.
riemann Matrix associated with the Riemann hypothesis.
ris Ris matrix -- a symmetric Hankel matrix.
smoke Smoke matrix -- complex, with a "smoke ring" pseudospectrum.
toeppd Symmetric positive definite Toeplitz matrix.
toeppen Pentadiagonal Toeplitz matrix (sparse).
tridiag Tridiagonal matrix (sparse).
triw Upper triangular matrix discussed by Wilkinson and others.
wathen Wathen matrix -- a finite element matrix (sparse, random entries).
wilk Various specific matrices devised/discussed by Wilkinson.
(Two output arguments)
GALLERY(3) is a badly conditioned 3-by-3 matrix.
GALLERY(5) is an interesting eigenvalue problem. Try to find
its EXACT eigenvalues and eigenvectors.
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