Enclosing the square root of a positive definite symmetric matrix

Abstract

The positive definite symmetric square matrices have unique square roots. This paper describes two iterative methods using the concepts of interval analysis for enclosing the square root S of a positive definite symmetric square matrix A. By this, we mean A = S ². The second method is tested on a numerical example and its results are given. Convergence theorems are established to show that both methods give two monotone sequences converging from both sides to the unique square root of A

Keywords:

• Symmetric
• matrix
• positive definite
• monotone
• cone
• square root