Data Sparse Matrix Computations - Lecture 4

domain ΩT domain ΩS "well-separated" xi yi Specifically, let’s say we have domains ΩS of N source points and ΩT of M target points, and these domains are “well-separated” (we will formalize this in section 3). Our goal is to compute the influence of all source points onto target points. Let the M × N matrix [K]ij = K(xi, yj) and assume it is approximately low-rank, so that K ≈ UV T with U of size M × P and V of size N × P . If P is small then we can efficiently compute the effect of many points in the source domain on points in the target domain. This low rank assumption is the same as saying that we can represent K with a function of x only and a function of y only K(x, y) ≈ P ∑