Skip to main content

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

From: Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations

  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
ACDC LU + ((15 N 2 +4N)KN(N-1)+4/3 N 2 K+ N 3 + N 2 ) N s 1
  +((33 N 2 +7N)KN(N-1)+4/3 N 2 K+ N 3 + N 2 ) N s 2
JD LU + 3 N 3 K+(4NK+N-2K)N(N-1) N s 1
  +((5 N 2 +16N-7)K+4N)N(N-1) N s 2
JD QR + 3 N 3 K+(6NK+2.5N+1.5K)N(N-1) N s 1
  +((5 N 2 +15.5N+21)K+7N)N(N-1) 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 ACDC LU + , JD LU + , and JD QR + , N s 1 is the number of sweeps without nonnegativity constraint; N s 2 is the number of sweeps with explicit nonnegativity constraint.