QR decomposition via givens rotations

Abstract

Different forms of Givens rotations have been proposed and available in the publishing industry. In this paper we derive via Pythagoras and Taylor series expansion to establish a noble ideal on the derivation of Givens rotations using elementary but classical framework to establish this novel idea. We propose an inverse Givens rotations(IGR) based on matrix inversion, the proposed IGR is application dependent and fit in easily on systolic array implementation and show similar operational characteristics with the existing methods such as the scaled GR.This technique is numerical stable and robust.