Inversion Free Algorithms for Computing the Principal Square Root of a Matrix. (18th June 2014)

• Record Type: Journal Article
• Authors: Assimakis, Nicholas; Adam, Maria
• Other Names: Verma Ram U. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2014(2014)
• Publication Date: 2014-06-18
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2014/613840
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : New algorithms are presented about the principal square root of ann × n matrixA . In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.