Sentence examples for bases for the subspaces from inspiring English sources

Given bases for the subspaces, unified alternative methods are conceived.

These methods are independent of the decompositions required to obtain the bases for the subspaces.

The anti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the subspaces of approximate solutions.

To describe the algebraic problem to which the equation leads, let ({varphi^{s}_{i}theta^{m}_{j}}) be a tensor product local basis function system for (Q^{k}(I_{i}times J_{j})), where ({varphi^{s}_{i}}_{s=1}^{k}) and ({theta^{m}_{j}}_{m=1}^{k}) are bases for the subspaces (P^{k}(I_{i})) and (P^{k}(J_{j})), respectively.

These previous researches considered the second kind of equations and constructed piecewise polynomials as bases for the subspaces of the Sobolev spaces (H^{m}_{0}(0,1)) consisting of elements satisfying the homogeneous boundary conditions u^{(j)}(0) = u^{(j)}(1) = 0, quadmbox{for }j=0, 1, ldots, m-1.

For (p=1), the set of ({overline{Psi}_{00}, overline{Psi }_{10}, overline{Psi}_{11}}) is represented as the multilevel bases for the subspace (S_{2}).

The representation of such subspaces, however, is far from being unique and our interest is to find the most localized bases for these subspaces.

The matrix sign function is thus revealed as an effective technique for applications in which bases for the deflating subspaces are required.

The columns of U and V give bases for the four fundamental subspaces.

These functions form orthonormal bases for the finite-dimensional subspaces (S_{n}) of the solution space (H^{1}_{0}(varOmega )).

These anti-derivatives form bases for the finite-dimensional subspaces of Sobolev space (H^{1}) and are used to construct an algorithm for approximating solutions.