有理参数曲面的移动平面与奇点

参数线性时不变系统频域模型降阶的贪心有理逼近

Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems

本文提出一种基于贪心策略的有理函数逼近方法，用于参数LTI系统的频域模型降阶，通过降阶基方法实现低阶有理函数构造。

两种参数分段有理插值核用于图像放大

Two kinds of parametric piecewise rational interpolation kernels for image magnification

本文提出两种参数分段有理插值核用于图像放大，其中一种核在PSNR、SSIM和FSIM指标上优于传统三次插值核。

Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy consists in constructing an explicit rational approximation based on few snapshots of the solution, in an interpolatory fashion. Under some restrictions on the structure of the original problem, we describe a priori convergence results for our technique, hereafter called minimal rational interpolation, which show its ability to identify the mai…

Parametric model reduction via rational interpolation along parameters

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the standard approach where transfer function interpolation is achieved for a discrete set of parameter and frequency samples. We accomplish this goal by using parameter-dependent projection spaces. Our main result shows that for holomorphic system matrices, the corresponding interpolatory projection spaces are also holomorphic. The coefficients of the power series rep…

Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a …

Spectral mesh-free quadrature for planar regions bounded by rational parametric curves

This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region's boundary curves corresponding to Green's theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green's theorem line integral. We present two methods to compute the intermediate quadrature r…