Circular Interval Arithmetic Applied on LDMT for Linear Interval System

The paper considers the LDMT Factorization of a general nxn matrix arising from system of interval linear equations. We paid special emphasis on Interval Cholesky Factorization. The basic computational tool used is the square root method of circular interval arithmetic in a sense analogous to Gargantini and Henrici as well as the generalized square root method due to Petkovic which enables the construction of the square root of the resulting diagonal matrix. We also made use of Rump’s method for multiplying two intervals expressed in the form of midpoint-radius respectively. Numerical example of matrix factorization in this regard is given which forms the basis of discussion. It is shown that LDMT even though is a numerically stable method for any diagonally dominant matrix it also can lead to excess width of the solution set. It is also pointed out that in spite of the above mentioned objection to interval LDMT it has in addition , the advantage that in the presence of several solution sets sharing the same interval matrix the LDMT Factorization requires to be computed only once which helps in saving substantial computational time. This may be found applicable in the development of military hard ware which requires shooting at a single point but produces multiple broadcast at all other points.