DocumentCode :
1561820
Title :
Fast algorithms to QR factor circulant matrices
Author :
Demeure, Cédric J. ; Scharf, Louis L.
Author_Institution :
Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA
fYear :
1989
Firstpage :
1123
Abstract :
The authors introduce a fast algorithm for computing the QR factors of a complex vertically circulant matrix C. The complexity of the algorithm is 5mn+2n2+O( m) complex-fixed point operations or 3mn+n 2+O(m) complex floating-point operations, where m is the number of rows in C and n is the number of columns (it is supposed that m<n). This algorithm can be used to solve overdetermined systems in the least-squares sense and to find an orthogonal basis spanning the same subspace as the columns of C. The matrices Q and R can be computed independently if desired. The authors also introduce a block QR factorization with two-by-two blocks, which is based on the split Levinson algorithm
Keywords :
matrix algebra; QR factor circulant matrices; block QR factorization; complex floating-point operations; complex vertically circulant matrix; complex-fixed point operations; fast algorithm; least-squares; orthogonal basis; overdetermined systems; split Levinson algorithm; Contracts; Convolution; Digital signal processing; Equations; Fixed-point arithmetic; Least squares methods; Linear systems; Signal processing algorithms; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1989. ICASSP-89., 1989 International Conference on
Conference_Location :
Glasgow
ISSN :
1520-6149
Type :
conf
DOI :
10.1109/ICASSP.1989.266630
Filename :
266630
Link To Document :
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