ISSN:
0945-3245
Keywords:
15A57
;
15A48
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary It was recently shown that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix. On the other hand, as it is well-known that the inverse of a strictly diagonally dominant Stieltjes matrix is a real symmetric matrix with nonnegative entries, it is natural to ask, conversely, if every strictly diagonally dominant Stieltjes matrix has a strictly ultrametric inverse. Examples show, however, that the converse is not true in general, i.e., there are strictly diagonally dominant Stieltjes matrices in ℝ n×n (for everyn≧3) whose inverses are not strictly ultrametric matrices. Then, the question naturally arises if one can determine which strictly diagonally dominant Stieltjes matrices, in ℝ n×n (n≧3), have inverses which are strictly ultrametric. Here, we develop an algorithm, based on graph theory, which determines if a given strictly diagonally dominant Stieltjes matrixA has a strictly ultrametric inverse, where the algorithm is applied toA and requires no computation of inverse. Moreover, if this given strictly diagonally dominant Stieltjes matrix has a strictly ultrametric inverse, our algorithm uniquely determines this inverse as a special sum of rank-one matrices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01385764
Permalink
