The author presents a polynomial-based algorithm for high-order multidimensional interpolation at the coarse-fine interface in the context of adaptive mesh refinement on structured Cartesian grids. The proposed algorithm reduces coarse-fine interpolation to matrix-vector products by exploiting the static mesh geometry and a family of nonsingularity-preserving stencil transformations. As such, n...

In the above paper [1], equation (8) should be = u x u x v y v y 1 r ij dxdudydv = z 3 3 6 p 2 0 1 qS q p 2 + 1 + 6 q 2 0 1 pS p q 2 + 1 + 6pS(p) + 6qS(q) 0 12pqT

In this paper we summarize the main results of where an algo rithm of shape preserving C spline interpolation for arbitrary D discrete data is developed We consider a classi cation of such data to separate the sec tions of linearity the angles and the breaks For remaining data we give a local algorithm of C interpolation by generalized splines with automatic choice of the parameters to retain t...

$EVWUDFW Digital image interpolation techniques are frequently used to enlarge pictures, i.e. zooming in, and they are upon increasingly demand for developing product applications using digital still cameras. One common difficulty with conventional interpolation techniques is that of preserving details, i.e. edges, and at the same time smoothing the data for not introducing spurious artifacts. ...

A new mathematical justification for using real interpolation points in model reduction is given, with the help of optimal time function approximations by transformed Legendre polynomials. Based on that, two reduction schemes are proposed: The first one applies a projection to the original model and matches 2q moments, similar to known rational Krylov methods. The second one matches q moments w...

We use bivariate C 1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and suucient condition on Bernstein-B ezier polynomials, we set the convexity preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on t...

An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in noncanonical Hamiltonian/Poisson form discretized space by finite differences. resulting system of ordinary differential equations integrated time average vector field (AVF) method. Poisson structure exhibits a skew-symmetric matrix depending on stat...

We present ongoing work to extend proof tree preserving interpolation to inductive sequences and tree interpolants. We present an algorithm to compute tree interpolants inductively over a resolution proof. Correctness of the algorithm is justified by the concept of partial tree interpolants and the appropriate definition of a projection function for conjunctions of literals onto nodes of the tr...

Inverse solutions to interpolation techniques in computer graphics may increase the accuracy of the rendered frames. An example is the use of an arbitrary time stamp in time interpolation to evaluate the t-parameter, which in turn can be used for time-variant spatial interpolation. In this paper, an analytic inverse is presented for a shape-preserving piecewise cubic Hermite interpolant, used i...