Finite Dimensional Operators

Operators are mappings from one Function Space to another. Finite Dimensional Operators are operators which map one discrete function to another. These are common in numerical analysis because the equations of physics are frequently approximated by this type of operator so that the equations may be solved on machines with finite memory.

The general finite dimensional operator may be written:

 g=Of

 g_i = o_i(f_0,...,f_n)

where the f_j are the values of the discrete function f, and the g_i are the values of the discrete function g. The operator is determined by the functions o_i. A linear finite dimensional operator is a matrix.

Finite Dimensional Operators provide all of the member functions that the Operator provides, e.g. apply, getDerivative, etc. In addition, the following functions are supported:

int getDimensionOfRange() const;
int getDimensionOfDomain() const;
NALinearMatrix *getDerivativeAsLinearMatrix(const NAFunction*,NALinearMatrix*) const;
NALinearFunctional *getConstantAsVector(const NAPointOnManifold*,NALinearFunctional*) const;

Finite Dimensional Operators have two dimensions: the dimension of the domain, and the dimension of the range. These are simply the dimensions of the discrete functions in the domain and range.

Examples of Finite Dimensional Operators include:

Linear Finite Difference Operators
Variable Linear Finite Difference Operators

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