Polynomial approximation and quadrature on geographic rectangles
نویسندگان
چکیده
Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theory of admissible meshes for multivariate polynomial approximation, we study product Gaussian quadrature, hyperinterpolation and interpolation on some regions of Sd, d ≥ 2. Such regions include caps, zones, slices and more generally spherical rectangles defined by longitudes and (co)latitudes (geographic rectangles). We provide the corresponding Matlab codes and discuss several numerical examples on S2.
منابع مشابه
Numerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature.
The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...
متن کاملBin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
We study the following packing problem: Given a collection of d-dimensional rectangles of specified sizes, pack them into the minimum number of unit cubes. We show that unlike the one-dimensional case, the two-dimensional packing problem cannot have an asymptotic polynomial time approximation scheme (APTAS), unless P = NP . On the positive side, we give an APTAS for the special case of packing ...
متن کاملImproved Pseudo-Polynomial-Time Approximation for Strip Packing
We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be ro...
متن کاملOn Weighted Rectangle Packing with Large Resources
We study the problem of packing a set of n rectangles with weights into a dedicated rectangle so that the weight of the packed rectangles is maximized. We consider the case of large resources, that is, the side length of all rectangles is at most 1 and the side lengths of the dedicated rectangle differ by a factor of at least 1="4, for a fixed positive " > 0. We present an algorithm which finds...
متن کاملChips on wafers, or packing rectangles into grids
A set of rectangles S is said to be grid packed if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 297 شماره
صفحات -
تاریخ انتشار 2017