修正後秩表現QR分解在遞迴最小平方法上的計算

Abstract

本文的目的在於利用秩表現QR分解法求 rank deficient 遞迴最小平方法 的問題.我們利用秩表現QR分解, 奇異值的插入定理, 以及兩種奇異值逼 近法 ACE 和 ICE 發展出一套新的演算法來解 rank deficient 遞迴最小 平方法的問題. Finding the numerical rank of a matrix is one of the moste problems in numerical linear algebra. The rankctorization (RRQR) can sometimes be used as a reliable and efficient computational alternative to the singular value decomposition (SVD) for problems that involve rank determination. In this thesis, we consider solving theeficient recursive least squares (RLS) problems with RRQR factorization. A new procedure is developed to generalize the full rank RLS problem to rank deficient cases. Our result ison the RRQR factorization proposed by Chan, the singularterlacing theorem and two dynamic condition estimators, algorithm by Bischof.