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It is well known that differential equations in one dimension can be solved efficiently with Chebyshev discretizations, O(N) operations for N unknowns, however this efficiency is lost in higher dimensions due to the coupling between modes.
If these conditions are not fulfilled we showed that the optimization can be solved efficiently with linear optimization algorithms.
The design conditions are expressed in terms of linear matrix inequalities which can be solved efficiently with available solvers.
These conditions result in convex linear matrix inequalities (LMIs) that can be solved efficiently with optimization techniques.
Given sufficient (but limited) measurements, it yields well-posed systems of nonlinear equations that can be solved efficiently with optimization.
Furthermore, it could not be solved efficiently with off-the-shelf optimization tools, and an ad-hoc metaheuristic had to be developed to (approximately) solve realistic-sized instances.
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The remaining issue concerns the choice of when to switch from one interval genotype to another, which is solved efficiently with a technique called "dynamic programming", a relative of a partitioning method used with hidden Markov models.
That this problem can be solved efficiently by a quantum computer is demonstrated with Simon's oracle.
These equations must be solved efficiently to fit large model spaces and models with large numbers of parameters.
(36)–(40) with boundary and initial conditions can be solved efficiently by the finite difference method.
With parameters specified, problem (4) can be solved efficiently by the block coordinate descent algorithm presented in Additional file 1: S4.3, Algorithm S1.
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