Perturbing tridiagonal M-matrices while maintaining inverse non-negativity
LE3 .A278 2008
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
An M-matrix is a special matrix with the properties that the non-diagonal entries are all non-positive, and that its inverse is element-wise non-negative. This property of having a non-negative inverse is one of the things that make M-matrices useful, but what if an application yields a matrix which is very close to being an M-matrix? Can we still say anything about its inverse? In this thesis we look at what happens to the inverses of tridiagonal M-matrices if small perturbations are made in different areas of the matrices, and find restrictions on the size of these perturbations such that the inverses will remain non-negative. In Chapter 3 we find restrictions on the size of single element perturbations. In Chapter 4 we examine the size of perturbations that can be made to a diagonal of the matrix. We will also explore some of the numerical techniques used to support our findings.
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