Returns the Border matrix
A = makematrix_border ( n )
a 1-by-1 matrix of doubles, integer value, the size of the matrix to return
a n-by-n matrix of doubles, the Border matrix
Returns the Border matrix of size n.
For i=1,2,...,n and j=1,2,...,n, if i==j, then
A(i,j) = 1
else if i<>n and j==n, then
A(i,j) = 2^(1-i)
else if j<>n and i==n, then
A(i,j) = 2^(1-j)
"The matrix has (n-2) eigenvalues at 1. Wilkinson (1965, pp 94-7) gives some discussion of this property."
J.C. Nash, Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, second edition, Adam Hilger, Bristol, 1990 (Appendix 1).