摘要
The conjugate decomposition(CD),which was given for symmetric and positive definite matrices implicitly based on the conjugate gradient method,is gen-eralized to every m×n matrix.The conjugate decomposition keeps some S VD prop-erties,but loses uniqueness and part of orthogonal projection property.From the com-putational point of view,the conjugate decomposition is much cheaper than the SVD.To illustrate the feasibility of the CD,some application examples are given.Finally,the application of the conjugate decomposition in frequency estimate is given with comparison of the SVD and FFT.The numerical results are promising.
基金
The work was partially supported by the CNPq,CAPES,and Foundação Araucária,Brazil,and NSFC11001128,China
Authors like to give their thanks to the referees for their helpful comments and suggestions to improve the quality of the paper.Authors also thank Professors Yu-Hong Dai,JoséMario Martinez,and Yaxiang Yuan for their helpful discussions and suggestions which help us to improve the quality of this article and further research issues.
