Parallel Jacobi-like algorithms are presented for computing a singular-value decomposition of an $mxn$ matrix $(m \geq n)$ and an eigenvalue decomposition of an $n x n$ symmetric matrix. A linear array of $O(n)$ processors is proposed for the singular-value problem and the associated algorithm requires time $O(mnS)$, where $S$ is the number of sweeps (typically $S \leq 10)$. A square array of $O(n^{2})$ processors with nearest-neighbor communication is proposed for the eigenvalue problem; the associated algorithm requires time $O(nS)$. Key Words And Phrases: Multiprocessor arrays, systolic arrays, singular-value decomposition, eigenvalue decomposition, real symmetric matrices, Hestenes method, Jacobi method, VLSI, real-time computation, parallel algorithms.
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机译：提出了类似Jacobi的并行算法，用于计算$ mxn $矩阵$（m \ geq n）$的奇异值分解和$ n x n $对称矩阵的特征值分解。提出了一个$ O（n）$处理器的线性数组用于奇异值问题，并且相关算法需要时间$ O（mnS）$，其中$ S $是扫描次数（通常为$ S \ leq 10）$ 。针对特征值问题，提出了具有最近邻通信的$ O（n ^ {2}）$处理器的方阵；相关算法需要时间$ O（nS）$。关键词和短语：多处理器数组，脉动数组，奇异值分解，特征值分解，实对称矩阵，Hestenes方法，Jacobi方法，VLSI，实时计算，并行算法。
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