finding a vector subsetinapproximability boundapproximation schemenormed space.The problem under study is, given a finite set of vectors in a normed vector space, find a subset which maximizes the norm of the vector sum. For each lp norm, p ∈[1,∞) the problem is proved to have an in...
Vnormalized = normalize(V,2,'norm'); % scales every row to have unit 2-norm Next, for each vector, we need to find a new vector that will NEVER be parallel to the vectors in Vnormalized. I'll be tricky here, to insure we will always succeed. The idea will be to find the ...
We present a randomized approximation algorithm for the problem of finding a subset of a finite vector set in the Euclidean space with the maximal norm of the sum vector. We show that, with an appropriate choice of parameters, the algorithm is polynomial for the problem with every fixed dimens...
from skyfield.api import load,EarthSatellite,wgs84, Topos from skyfield.positionlib import Geocentric from numpy.linalg import norm def normalize(vector): return vector / norm(vector) def find_earth_intersect_point(origin,vector,earth_radius): #Step 1: Turn that vector into a unit vector. Still...
For a matrix M and vectors x^{(i)}, i\in I, we define \Delta (M;x^{{(i)}}, i\in I) = ||M||_F^2 - ||M - M\sum_{i\in I}x^{(i)}x^{(i)^T}||_F^2 \\ When x^{(i)} are orthonormal vectors, this represents the norm of the projection of M onto the ...
Find a subset of vectors X of cardinality m such that the norm of the sum of the vectors from X is maximum.The second problem is connected in a signal search in a sequence of im- pulses with additional noise problem [1]. This problem has applications in 关键词: Euclidean space vector ...
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher...
Figure 1 could be used for discussing the first of them. It shows the Euclidean norm of the numerical gradient error, calculated by forward finite difference, when compared with the analytic solution derived in this study. This error is presented as a function of the step size employed, in ...
rows(uvec(std::vector<arma::uword>{subspot_idx }))), 1); // Get neighbors. const uvec neighbor_idx = (man_dist < dist) && (man_dist > 1e-6); if (accu(neighbor_idx) < 2) { throw std::runtime_error("Error in finding neighbors of subspots!"); } subspot_neighbors.emplace...
Let A, B ⊂ Rn be compact convex sets. Consider the minimal number t0 > 0 such that t0B covers A after a shift to a vector x0∈ Rn. The goal is to find t0 and x0. In the special case of B being a unit ball centered at zero, x0 and t0 are known as the Chebyshev ...