Many polynomial systems have solution sets comprised of multiple irreducible components, possibly of different dimensions. A fundamental problem of numerical algebraic geometry is to decompose such a solution set, using floating-point numerical processes, into its components. Prior work has shown how to generate sets of generic points guaranteed to include points from every component. Furthermo...

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Pre-processing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data cases. Recently, deep learning has been used address the interpolation problem at expense of large amounts training adequately represent typical events. Nonetheles...

The Skorokhod distance is a natural metric on traces of continuous and hybrid systems. For two traces, from [0, T ] to values in a metric space O, it measures the best match between the traces when allowed continuous bijective timing distortions. Formally, it computes the infimum, over all timing distortions, of the maximum of two components: the first component quantifies the timing discrepanc...

In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. main improvement is that can allow general interpolation couples. The abstract applied to regularity problems fractional equations stochastic equations, where uniform trace est...

Starting from a 2-D interpolation scheme presented elsewhere in this report, we develop an algorithm for interpolation of 3-D data. Spatial prediction lters are used to estimate the apparent dip between pairs of traces. These dip estimates are combined to give a local estimate of the true dip in 3-D, which is then used to perform interpolation.

Missing trace reconstruction is a challenge in seismic processing due to incomplete and irregular acquisition. Noise is a concern, due to the many sources of noise that occur during seismic acquisition. Most of the recent research on denoising and interpolation focuses on transform domain approaches using L1 norm minimization. A specific kind of constraint, called the synthesis approach, is wid...

The standard Chimera Domain Decomposition approach to numerically solving the conservation laws of uid dynamics can give rise to anomalous ow eld features near subdomain boundaries. Keeling, Tramel, and Benek hypothesized that these anomalous behaviors are caused by interpolation across shocks at the artiicial boundaries and can be eliminated by using the appropriate trace approximation near sh...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis, and computational biology (e.g., protein folding), just to name a few application areas. We propose a linear-time randomized algorithm for approximating the tra...