Exact(16)
The shortest paths may have different path lengths (l k = 0, l k = 1, l k = 2, l k = 3, etc).
Here, I is the L k × L k identity matrix.
Assume D k ∗ = L k ∗ L k ∗ ′ + Ψ k ∗, with L k ∗ the matrix consisting of the first m k columns of the Cholesky factor of D k ∗.
We only have to show that L k ( G ) = L k ( U ) + L k ( V ).
where r o ≫ l k.
This is equivalent to X l, k = a l, k ⋅ H l, k + n l, k (4).
Similar(44)
Proof Let l ≤ k.
Case 1. l = k.
for all L ∈ K o n.
for each L ∈ K 0 n.
(l − k ) ! standing for the binomial factor.
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