Sentence examples for both gradient and function from inspiring English sources

It is easy to conclude that this formula contains both gradient and function value information.

It is clear that the quasi-Newton equation (1.10) also contains both gradient and function value information, and it has been proved that the new formula has a higher order approximation to (nabla^{2} f(x)).

CGP methods are particularly useful in MIMO systems, as the solutions can be found using gradients and functions of complex-valued matrix variables.

The conditions for Clarke's generalized gradient and the functions are the same as in (j1)–(j1).

This complexity could be achieved by introducing in the scaffolds gradients of morphology, composition' and function.

In the shape optimization process, we carry out frequency response analysis to calculate shape gradient function, and then use the shape gradient functions in velocity analysis to update the shape or position of the inlaid material based on the H1 gradient method.

Under the assumption that each member varies in the out-of-plane direction to its centroidal axis, the shape gradient functions and the optimality conditions are theoretically derived by the Lagrange multiplier method and the formulae of the material derivative.

Ductile particles are dispersed in form of various gradient functions, and the composite samples were loaded under uniaxial tension.

The mitigating effect of DGPF coating with respect to design parameters such as average density, density difference (uneven density), gradient functions and load intensity is explored.

Both PCR reactions were optimised using the machine's gradient function, and amplicon size as well as specificity was confirmed by agarose gel electrophoresis (data not shown).

In fact, the objective function, its gradient, and Hessian can also be vectorized, making the implementation very efficient.