Robust array interpolation using second-order cone programming
We study Friedlander's (1993) array interpolation technique, whose main shortcoming in multisource scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. In this letter, we develop a new robust interpolation approach by minimizing the interpolation error inside the sectors of interest while setting multiple "stopband" constraints outside these sectors to prevent performance degradation effects caused by out-of-sector sources. Computationally efficient convex formulations of the robust interpolation matrix design problem using second-order cone programming are derived.
Abstract This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, min-max boxes, and surface/surface intersections. The class of surfaces that can be handled are all parametric C 2 surfaces. All the algorithms are related by theorems from approximation theory which give information about the maximum deviation an approximation to a surface can have if bounds on partial derivatives are known. We generalize these theorems to work with parametric geometry, and we also show how to obtain the necessary bounds.