On computing complex square roots of real matrices

On computing complex square roots of real matrices

We present an idea for computing complex square roots of matrices using only real arithmetic.

Logarithms and Square Roots of Real Matrices

The need for computing logarithms or square roots of real matrices arises in a number of applied problems. A significant class of problems comes from medical imaging. One of these problems is to interpolate and to perform statistics on data represented by certain kinds of matrices (such as symmetric positive definite matrices in DTI). Another important and difficult problem is the registration ...

Computing the Square Roots of a Class of Circulant Matrices

Computing the square roots of matrices with central symmetry

For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are based on the Schur decomposition of A, were proposed by Björk and Hammarling [3], for square roots of general complex matrices, and by Higham [10], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of m...

On Square Roots of M-Matrices

The question of the existence and uniqueness of an M-matrix which is a square root of an M-matrix is discussed. The results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an M-matrix.