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So if we find some relative rules such that the second term of the problem (3) has the same properties with the same variable as the first term, one approximate solution of (3) can be easily found similar as classic shrinkage.
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It is obvious that the first term of the problem (3) is additive and separable.
Note that the first term of the above problem indicates the underlying vector is close to the known vector (( {mathbf{x}}^{(t)}-{mathbf{u}}_2^{left t-1right)} )) in Euclidean norm, and the second term is an indicator function; the optimal solution to the above problem is {mathbf{y}}^{(t)}={P}_Sleft({mathbf{x}}^{(t)}-{mathbf{u}}_2^{left t-1right)}right).
The overall stochastic programming problem can be divided into two subproblems: 1) the investment subproblem in the first and second terms of the defined objective; 2) the operating subproblem in the third and fourth terms of the defined objective.
For a noisy observation, however, small eigenvalues ζ uv can lead to significant noise amplification in the second term of (4) so the inverse problem becomes ill-posed.
The Democrats portray Mr. McCain as offering a third Bush term, but it's a third term of the war that's his bigger problem.
The first term of problem (9) is the data consistency, and the second term represents sparse representation regularization term in the TIHP tight frame.
The first term of problem (6) is the data consistency, which enforces the Fourier magnitude constraint.
where and are the first and the second terms of max-min optimization problem in (12).
The first terms of the perturbation series lead to the linear problem.
For simple problems, where the first term of your trinomial is just x 2, the terms in the First position will always be x and x.
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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