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. 2023 Oct 31;127(44):9346–9356. doi: 10.1021/acs.jpca.3c04363

Table 3. Construction of an m-Gaussian Model for a Gaussian Density.

Step Description Equations Cost
1 Input Inline graphic   O(1)
  If ρ is spherical    
2a Compute ⟨uj⟩ and β0 (42), (43) O(m)
3a Compute initial guess for β (44) O(m2)
4a Set B = 0   O(m)
  else if ρ is cylindrical    
2b Sort primitives by |di| value   O(n)
3b Compute initial guess for β and B   O(m)
  end if    
5 Compute f00, f10, f01, f20, f11, f02 (33), (52)–(56) O(m)
6 Compute F00, F10, F01, F20, F11, F02 (34), (52)–(56) O(m2)
7 Compute E10, E01, E20, E11, E02 (59) – (63) O(m)
8 Compute U10, U01, H20, H11, H02 (59) – (63) O(m3)
9 Compute x (37) O(m3)
10 Compute g (57) O(m2)
11 Compute H (58) O(m3)
12 Compute (βB) ← (βB) – Δ (69) O(m3)
13 If |Δ| > 10–4 or H is not positive definite, go to Step 5   O(m3)