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

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

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

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

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

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

$3N^{3}K+(4\mathit{\text{NK}}+N-2K)N(N-1)N_s^1$

$+\left(\right(5N^2+16N-7)K+4N)N(N-1)N_s^2$

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

$3N^{3}K+(6\mathit{\text{NK}}+2.5N+1.5K)N(N-1)N_s^1$

$+\left(\right(5N^2+15.5N+21)K+7N)N(N-1)N_s^2$