Two ways to extend the Cholesky decomposition to block matrices with interval entries (Q1604709)

Two ways are presented to extend the Cholesky decomposition to block matrices with interval entries. One is similar to the block Cholesky decomposition, another is a mixture of the block interval Gaussian algorithm and the square roots of matrices. Feasibility results are shown for both of them and compared to each other. These block interval Cholesky decompositions can be used to bound the solutions of linear systems of equations with symmetric block matrices and right-hand sides both of which are varying within given intervals.