Search results
Results from the WOW.Com Content Network
one can calculate a single point (e.g. the center of an image) using high-precision arithmetic (z), giving a reference orbit, and then compute many points around it in terms of various initial offsets delta plus the above iteration for epsilon, where epsilon-zero is set to 0.
This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
For example, suppose X is the set of points in the two-dimensional plane, R is the set of closed filled rectangles (products of closed intervals), and P is the unit square [0, 1] × [0, 1]. Then the set N consisting of the 8 points shown in the adjacent diagram is a 1/4-net of P, because any closed filled rectangle intersecting at least 1/4 of ...
Isomap on the “Swiss roll” data set. (A) Two points on the Swiss roll and their geodesic curve. (B) The KNN graph (with K = 7 and N = 2000) allows a graph geodesic (red) that approximates the smooth geodesic. (C) The Swiss roll "unrolled", showing the graph geodesic (red) and the smooth geodesic (blue). Replication of Figure 3 of [1].
In numerical analysis, the ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method [1] while retaining the optimal [2] worst-case performance of the bisection method. [3]
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]
The methods differ in their runtime complexity (below, n is the number of variables and epsilon is the accuracy): The circumscribed method requires O ( n 2 ) ln 1 ϵ {\displaystyle O(n^{2})\ln {\frac {1}{\epsilon }}} iterations, where each iteration consists of finding a separating hyperplane and finding a new circumscribed ellipsoid.