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.