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The direct optimization starts from an arbitrary guess pulse, see Section 3.2 for details.
For an arbitrary guess, the sequence is generated by the iterative algorithm (4.1).
First, the target gate depends on (hat {mathbf {U}}_{0}) induced by the (arbitrary) guess pulse, and second, the construction of the closest diagonal perfect entangler does not take into account the topology of the optimization landscape; the 'closest' gate is by no means guaranteed to be the one that is easiest to reach.
For a given arbitrary guess x 0 ∈ C and a sequence { α n } ∈ ( 0, 2 γ − L ), we also propose the following explicit scheme that generates a sequence { x n } in an explicit way: x n + 1 = P C [ θ n h ( x n ) + ( 1 − θ n ) T n x n ], n ≥ 0, (10).
What's interesting is that even if the anchor is an arbitrary guess, people still adjust around it.
Similar(7)
Instead, he says, they amount to arbitrary guesses, and misleading ones at that.
As a result, the conclusions generated by many CGE models of trade in services are so dependent upon arbitrary guesses as to border on arbitrary themselves.
where Z 0 ∈ X is an arbitrary initial guess of z 0 which is independent of the guess and Z ˜ ( n ) ( 0 ) denotes the value Z ˜ ( 0 ) at the n th iteration.
where Z 0 ∈ X is an arbitrary initial guess of z 0 which can be proved independent of the guess in the following text.
(4.4) where (x_{0}in C) is an arbitrary initial guess.
Starting with an arbitrary initial guess, generate a sequence by the following iterative scheme: (1.7).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com