Abstract The so-called DCD-matrices consist of products of two diagonal matrices with a circulant matrix, merging diagonal and circulant matrices with rank-one matrices. By introducing a notion of double orthogonality for rectangular matrices, an iterative double orthogonalization process is devised for approximating a given M \, C^n n M ∈ C n × n with DCD-matrices. This simultaneous orthogonality of columns and rows leads to several approximation schemes of which the best rank-one approximation is just a special case. Expanding through summing yields, like principal component analysis (PCA), a novel optimal technique for reducing the dimensionality of datasets. Being notably general and flexible, this approach provides a natural way to merge fast Fourier methods with low rank matrix approximations. Least squares solution methods play a significant role in algorithms.
Huhtanen et al. (Thu,) studied this question.