Sentence examples for dual basis from inspiring English sources

Functionals, form a dual basis for basis.

First, we want to describe the form of the dual basis.

The last one is that ({psi_{j,k}}) has a unique dual basis.

The construction of the dual basis must be repeated at each time the approximation polynomial increased.

Jüttler [7] represented the dual basis function with respect to the Bernstein basis.

Jüttler [7] derived an explicit formula for the dual basis function of Bernstein polynomials.

The keys for proving Theorem 3.4 are that the dual wavelet basis of the pre-wavelet basis has been constructed, and it has the same decay as the basis.

Under the decay condition, we have constructed the dual wavelet basis of a pre-wavelet basis.

From the matrix, B i, ∀ i ∈ I, one can build a dual code basis.

Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator.

The proof relies on the (L^{p} -boundedness of the frame operator of the duaL^{p} -boundednessich is an applicatiof from theorem 3.2.