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makematrix_border

Returns the Border matrix

Calling Sequence

A = makematrix_border ( n )

Parameters

n :

a 1-by-1 matrix of doubles, integer value, the size of the matrix to return

A :

a n-by-n matrix of doubles, the Border matrix

Description

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."

Examples

A = makematrix_border ( 5 )

Authors

Bibliography

J.C. Nash, Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, second edition, Adam Hilger, Bristol, 1990 (Appendix 1).


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