Quadrature-Based Vector Fitting for Discretized $\mathcal{H}_2$ Approximation
نویسندگان
چکیده
منابع مشابه
Quadrature-Based Vector Fitting for Discretized H2 Approximation
Vector Fitting is a popular method of constructing rational approximants designed to fit given frequency response measurements. The original method, which we refer to as VF, is based on a least-squares fit to the measurements by a rational function, using an iterative reallocation of the poles of the approximant. We show that one can improve the performance of VF significantly, by using a parti...
متن کاملVector Fitting for Matrix-valued Rational Approximation
Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and established a connection with optimal H 2 approximation. We build on this work and extend the previous framework to include the construction of effective rati...
متن کاملQuadrature-based features for kernel approximation
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach all...
متن کاملInterpolated Discretized Embedding of Single Vectors and Vector Pairs for Classification, Metric Learning and Distance Approximation
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and c) general, non-Euclidean, semimetric learning. To the best of our knowledge, this is the first work that enables learning any general, non-Euclidean, semim...
متن کاملApproximation and Quadrature
Let V be a vector space with inner product (u, v) and norm u = (u, u) 1/2. We are given u ∈ V and a subspace˜V = span v (n) are linearly independent. We want to find p ∈ ˜ V such that u − p is minimal.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2015
ISSN: 1064-8275,1095-7197
DOI: 10.1137/140961511