论文部分内容阅读
本文综述了有关修正的奇异值分解的算法和Systolic阵列实现的一些最新结果,讨论了普通奇异值分解(OSVD)、积奇异值分解(PSVD)和商奇异值分解(QSVD)。修正算法是指交叉使用QR更新和三角约化Jacobi SVD算法,在其每步计算中采用有限次操作(O(n~2)),由前一次近似分解结果计算新的近似分解。这些算法与指数加权相结合,显然对跟踪问题极为适用,而且只要对熟知的矩阵何量积、QR更新和SVD的Systo1ic阵列稍加修改,就能把它们完美地映射到Systolic阵列上去。
This paper reviews some recent results about the modified singular value decomposition algorithm and the Systolic array implementation. The general singular value decomposition (OSVD), product singular value decomposition (PSVD) and the singular value decomposition (QSVD) are discussed. The correction algorithm refers to the cross-use QR update and the triangular reduced Jacobi SVD algorithm, and uses a finite number of operations (O (n ~ 2)) in each step of calculation to calculate a new approximate decomposition from the previous approximate decomposition result. These algorithms, in combination with exponential weights, are obviously well suited for tracking problems and can be perfectly mapped to Systolic arrays with little modification to the well-known Matrix Geometries, QR Updates, and SVD Systo1ic Arrays.