In this paper, we construct a novel normalized B-spline-like representation for C-2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. With the help of the control polynomial theory introduced herein, a Marsden identity is derived, from which several families of super-convergent quasi-interpolation operators are defined. (C) 2021 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).
A new approach to deal with cubic splines and its application to super-convergent quasi-interpolation
S. Eddargani;
2022-01-01
Abstract
In this paper, we construct a novel normalized B-spline-like representation for C-2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. With the help of the control polynomial theory introduced herein, a Marsden identity is derived, from which several families of super-convergent quasi-interpolation operators are defined. (C) 2021 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).
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