A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a Gramian, is obtained efficiently orthogonalize the B-splines. The can be also used fast inversion method Gramian characterized by remarkable sparsity of matrix. There are two versions algorithm: first one more efficient and applicable Toeplitz while second general, works with any but computationall...

In this paper we consider spaces of bivariate splines of bi–degree (m,n) with maximal order of smoothness over domains associated to a two–dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor–product B–splines acting effectively on these domains. Following the strateg...

We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded meshes. By exploiting a local tensor product structure, we extend construction rules spline setting. The proposed algorithm has computational cost proportional number degrees freedom and advantageous properties increa...

In this paper some of the relationships between B-splines and linear control theory is examined. In particular, the controls that produce the B-spline basis is constructed and compared to the basis elements for dynamic splines.