# Systolic Approach for QR Decomposition

• Halil Snopce
• Azir Aliu
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 343)

## Abstract

In this paper we discuss the parallelization of the QR decomposition of matrices based on Given’s rotation using the iterative algorithm. For this purpose we have used the systolic approach. The mathematical background of the problem is followed by the parallelization which continues step by step as it is shown at Figs. 25.5 and 25.6. The output values of Fig. 25.5 become the input for Fig. 25.6 and vice versa, the output values of Fig. 25.6 become the input for Fig. 25.5. This kind of iteration is repeated until achieving the convergence.

## Keywords

QR decomposition Parallelization of QR decomposition Systolic array Given’s rotations Computing the orthonormal matrix Computing the upper triangular matrix

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