Bisection/Inverse iteration

Choose a matrix case

	A 8*8 matrix with the eigenvalues +/- 10sqrt(10405) (1020.049...) a double eigenvalue 1000 and two more eigenvalues near 1019 and 1020, that is a dense cluster of eigenvalues and in addition the eigenvalues 0 and 510-100sqrt(26)=0.09805.
	The "bar matrix" (quindiagonal matrix) with the diagonals 1,..,1; -4,...,-4; 5,6,..,6,5; -4,...,-4; 1,...1, and the analytically known eigenvalues 16*sin(i*pi/(2(n+1)))**4, i = 1,...,n.
	Generation of a matrix from a given fixed unitary eigensystem Rij = (sin(ij*pi/(n+1))*sqrt(2/(n+1)), i,j = 1,...,n and freely chooseable eigenvalues. The entries must be separated by comma or blank If an eigenvalue Ei occurs m times then you might use the following shorthand notation: E1,...,m*Ei,...,En eigenvalues:
	Input of a symmetric matrix via its lower triangle: The data must be given rowwise, each new row beginning on a new line. But a single row may extend over several lines. Entries to be separated by comma or blank. A= 2, -1,1, 0,3,4 The example is for n=3.
	Direct input of a tridiagonal matrix via its diagonal and its first superdiagonal in turn, hence A(1,1),A(1,2),A(2,2),A(2,3),...,A(n,n) Entries to be separated by comma or blank. if a value W occurs m times in succession, you might use the shorthand notation ..,m*W,.... diagonals:

Please specify in the cases 2, 3, 4 and 5 the dimension of the matrix:
n=
Important for the bar matrix (case 2) 5 <= n <= 30 and otherwise 2 < = n < = 30 !

Should the input matrix occur in the output?
no
yes

Should the eigensystem occur in the output ?
yes
no

Should the eigenvectors be subject to reorthogonalization during iteration?

yes
no

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