Table 1 Comparison of computational complexity

Matrix multiplication: K²d(2MN + N² + M²)

 ${\mathbf{U}}_k{\mathbf{U}}_k^H,{\mathbf{V}}_k{\mathbf{V}}_k^H,k\in \mathcal{K}$: Kd(M² + N²)

  P^I: K(K − 1)d²(min(M,N) + 1)

  ${\tilde{\mathbf{U}}}_k,{\tilde{\mathbf{V}}}_k,k\in \mathcal{K}$: Kd(2d + M + N)

Subproblem construction: 6K T^inner (M² + N²)

Eigenvalue decomposition: 9K(M³ + N³)

Compact SVD: K d²(14M + 14N + 16d)