In the paper: Bounded Biharmonic Weights for Real-Time Deformation in the first contact to the Euler-Lagrange equation, simply record it.
The definition of functional
A defined: Functional (Functional) generally refers to the domain of the function set, and the range of real or complex mappings. In other words, from a functional space defined by a vector function consisting of a scalar field mapping.
Definition of two: set \ (\ boldsymbol {C} \ ) is the set of functions (form), \ (\ boldsymbol {B} \) is the set of real numbers; if \ (\ boldsymbol {C} \ ) any one of elements \ (Y (X) \) , in \ (\ boldsymbol {B} \ ) in an element has \ (\ boldsymbol {J} \ ) corresponding thereto, called \ (\ boldsymbol {J} \ ) is \ (y (x) \) functionals, referred to as \ (\ boldsymbol {J} [Y (X)] \) .
Functional is a function of a function to function as independent variables, rather than ordinary variables
Shortest path: \ (\ boldsymbol {L} = \ {L} boldsymbol [Y (X)] \)
\(J[y(x)] = \int_a^b \sqrt{1 + y'^{2}} dx\)
The simplest functional: the following functional relationship as the most simple functional
\ (J [y (x)
] = \ int_a ^ b F (x, y, y ') dx \) wherein, \ (F. (X, Y, Y') \) is called the kernel function.
NOTE: Operator is a mapping function to another function, which is a vector from a vector space to space mapping; functional vector space from the log domain mapping; function number is a number from domain to domain mapping.
Reference:
"functional" What does that mean? - elegant answer referred White Hart - known almost
functional and the variational method