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Using dual or real, for m functions in n variables, the m functions need to be evaluated n times, once for each seeded variable. Thus, theoretically, O(m*n). In practice, however, there are problems in which not all functions depend on all variables. In such cases, it's possible to avoid function re-evaluations. This optimization is problem-dependent and has to be done manually by the user. |
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What is the time-complexity of Jacobian computation for mx1 vector and nx1 variables. Is it O(m*n)?
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