计算机科学
算法
收缩阵列
QR分解
信号处理
数字信号处理
并行计算
超大规模集成
特征向量
计算机硬件
量子力学
物理
嵌入式系统
作者
F. Lorenzelli,Kung Yao
摘要
High throughput parallel processing arrays are in increasing demand for a large number of applications, ranging from digital signal and image processing, to radar/sonar applications, Kalman filtering etc. Advances in VLSI technology together with the employment of parallel computing concepts make it possible to process large amounts of data at speeds which had been unimaginable before. Since general purpose machines still cannot face the requirements of high throughput and high computational loads, specific array processors have to be designed, with characteristics of regularity, locality of interconnection and high degree of concurrency. The most commonly used algorithms display common characteristics of regularity, which can be exploited in the design of the desired array processors. In this dissertation, we present a mapping methodology based on integral matrix theory, which systematically proceeds from the (piecewise) regular algorithm to the physical array, accounting for possible design constraints. A number of partitioning schemes ranging from the standard LSGP to the LPGS techniques can be obtained. Folding, in the sense of displacement of portions of processing units, is also included in the overall linear mapping procedure. The problem of correct control generation for the selection of data paths and computational functions is also considered.
Numerical QR-based techniques are then analyzed and systolic arrays which implement such algorithms are obtained. In particular, alternative designs implementing the QR algorithm for eigenvalues decomposition are derived using the mapping tools previously introduced. A rank revealing version of the QR factorization is analyzed and its possible applications to a number of problems such as subset selection, linear regression and frequency estimation are discussed. A slight variant on the rank revealing QR algorithm is the base of the RRQR systolic array derived and analyzed in this dissertation.
The Total Least Squares (TLS) problem arises in many fields of numerical analysis, linear regression, frequency estimation etc. The TLS problem is described and applications to clustering of data, system identification and linear and nonlinear regression are presented. The solution to the TLS problem can be obtained using the rank revealing QR factorization discussed in this dissertation.
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