# Table 1 Numerical complexities of seven JDC algorithms in terms of flops

Numerical complexity

ACDC

(13/3N3K+3N4+2N2K+N3+N2)N s

FFDIAG

(2N3K+N3+2N2K+4N(N-1))N s

LUJ1D

(4N K+N-2K)N(N-1)N s

QRJ1D

(6N K+2.5N+1.5K)N(N-1)N s

${\text{ACDC}}_{\text{LU}}^{+}$

$\left(\left(15{N}^{2}+4N\right)\mathit{\text{KN}}\left(N-1\right)+4/3{N}^{2}K+{N}^{3}+{N}^{2}\right){N}_{s}^{1}$

$+\left(\left(33{N}^{2}+7N\right)\mathit{\text{KN}}\left(N-1\right)+4/3{N}^{2}K+{N}^{3}+{N}^{2}\right){N}_{s}^{2}$

${\text{JD}}_{\text{LU}}^{+}$

$3{N}^{3}K+\left(4\mathit{\text{NK}}+N-2K\right)N\left(N-1\right){N}_{s}^{1}$

$+\left(\left(5{N}^{2}+16N-7\right)K+4N\right)N\left(N-1\right){N}_{s}^{2}$

${\text{JD}}_{\text{QR}}^{+}$

$3{N}^{3}K+\left(6\mathit{\text{NK}}+2.5N+1.5K\right)N\left(N-1\right){N}_{s}^{1}$

$+\left(\left(5{N}^{2}+15.5N+21\right)K+7N\right)N\left(N-1\right){N}_{s}^{2}$

1. (N, N, K): the dimensions of the three-way array . For ACDC, FFDIAG, LUJ1D, and QRJ1D, N s is the number of total sweeps. For ${\text{ACDC}}_{\text{LU}}^{+}$, ${\text{JD}}_{\text{LU}}^{+}$, and ${\text{JD}}_{\text{QR}}^{+}$, ${\mathit{\text{N}}}_{s}^{\text{1}}$ is the number of sweeps without nonnegativity constraint; ${\mathit{\text{N}}}_{s}^{\text{2}}$ is the number of sweeps with explicit nonnegativity constraint.
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