Consider linear algebraic systems where the elements of the matrix and the right-hand side vector depend linearly on a number of interval parameters. We prove some sufficient conditions for the united parametric solution set of such a system to have linear boundary. These conditions imply an equivalent representation of the parametric system where each parameter appears once in a diagonal matri...

Abstract—Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables...

A new frequency response based model reduction technique is presented for use in the mid-frequency range. The reduction was designed to avoid the use of modal based correlation metrics, which are known to fail in systems with high modal density. A transformation matrix based on a set of complex shapes extracted from the frequency response is used to reduce the impedance matrix to the sensor loc...

The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and boundary in what we call the R-matrix since quantity of interest reflection matrix (R-matrix). Given bulk S-matrix, space allowed R-matrices an infinite dimensional convex from which plot two section given by domain on 2d plane. In certain cases, at domain, find vertices corresponding integrable no free parameters. oth...