Figure Properties - SERC

toeppen—Pentadiagonal Toeplitz matrix (sparse)
gallery
P = gallery('toeppen',n,a,b,c,d,e) returns the n-by-n sparse,
pentadiagonal Toeplitz matrix with the diagonals: P(3,1) = a, P(2,1) = b,
P(1,1) = c, P(1,2) = d, and P(1,3) = e, where a, b, c, d, and e are scalars.
By default, (a,b,c,d,e) = (1,-10,0,10,1), yielding a matrix of Rutishauser.
This matrix has eigenvalues lying approximately on the line segment
2*cos(2*t) + 20*i*sin(t).
tridiag—Tridiagonal matrix (sparse)
A = gallery('tridiag',c,d,e) returns the tridiagonal matrix with
subdiagonal c, diagonal d, and superdiagonal e. Vectors c and e must have
length(d)-1.
A = gallery('tridiag',n,c,d,e), where c, d, and e are all scalars, yields the
Toeplitz tridiagonal matrix of order n with subdiagonal elements c, diagonal
elements d, and superdiagonal elements e. This matrix has eigenvalues
d + 2*sqrt(c*e)*cos(k*pi/(n+1))
where k = 1:n. (see [1].)
A = gallery('tridiag',n) is the same as
A = gallery('tridiag',n,-1,2,-1), which is a symmetric positive definite
M-matrix (the negative of the second difference matrix).
triw—Upper triangular matrix discussed by Wilkinson and others
A = gallery('triw',n,alpha,k) returns the upper triangular matrix with
ones on the diagonal and alphas on the first k >= 0 superdiagonals.
Order n may be a 2-element vector, in which case the matrix is n(1)-by-n(2)
and upper trapezoidal.
Ostrowski [“On the Spectrum of a One-parametric Family of Matrices, J. Reine
Angew. Math., 1954] shows that
cond(gallery('triw',n,2)) = cot(pi/(4*n))^2,
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