The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK library, suffer from performance limitations due to the use of matrix–vector type operations in the phase of panel factorization. These limitations can be remedied by using the idea of updating of QR factorization, rendering an algorithm, which is much more scalable and much more suitable for implementation on a multi-core processor. It is demonstrated how the potential of the cell broadband engine can be utilized to the fullest by employing the new algorithmic approach and successfully exploiting the capabilities of the chip in terms of single instruction multiple data parallelism, instruction level parallelism and thread-level parallelism.

中文翻译：

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细胞宽带引擎的QR分解

QR分解是稠密线性代数中最重要的运算之一，它提供了一种数值稳定的方法来求解方程式的线性系统，包括超定和欠定的系统。QR分解的现代实现（例如LAPACK库中的QR分解）由于在面板分解阶段使用矩阵-矢量类型运算而受到性能限制。这些局限性可以通过使用更新QR因数分解，渲染算法的思想来弥补，该思想具有更大的可扩展性并且更适合在多核处理器上实施。