Abstract:

The conjugate decomposition (CD), which was given for symmetric and
positive definite matrices implicitly based on the conjugate gradient method, is generalized
to every m×n matrix. The conjugate decomposition keeps some SVD properties,
but loses uniqueness and part of orthogonal projection property. From the computational
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.

Key words: Singular value decomposition, Conjugate decomposition , Generalized
inverse , Least squares solution , Projection , Orthogonal projection , Frequency
estimate , FFT