Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Matrix function”

Enhanced matrix function approximation

Eshghi, Nasim, Reichel, Lothar, Spalević, Miodrag · 2022

Matrix functions of the form f (A) v, where A is a large symmetric matrix, f is a function, and v not equal 0 is a vector, are commonly approximated by first applying a few, say n, steps of the symmetric Lanczos process to A with the initial vector v in order to determine an orthogonal section of A. The latter is represented by a (small) n x n tridiagonal matrix to which f is applied. This approach uses the n first Lanczos vectors provided by the Lanczos process. However, n steps of the Lanczos process yield n + 1 Lanczos vectors. This paper discusses how the (n + 1) st Lanczos vector can be used to improve the quality of the computed approximation of f (A) v. Also the approximation of expressions of the form v(T) f (A) v is considered.

Cited by 0

TFM: Transfer Function Matrix

Frank Willems, Bram De Jager · 2015

For surge control in compression systems, a suitable combination of actuators and sensors must be selected. The goal is to identify the combinations for which there exists a controller that locally stabilizes the linearized compression system model and meets additional control objectives. The latter are quantified in terms of a bound on an H∞-norm. With this, we aim to stay close to the nominal operating point in the face of disturbances, noise, and actuator limitations. The considered selection method is more rigorous than previously found in literature, in the sense that multivariable, dynamic output-feedback is the focus and that different performance specifications are handled simultaneously. Though the method was originally developed for linear systems, it can be used for the nonlinear compression system model, by linearizing the model on a grid of nominal operating points. Among the proposed actuators and sensors, the close-coupled valve and mass flow sensor are identified as the most promising. The results are sustained by the physics of the problem.

Cited by 0

Hierarchical matrix Lyapunov function

А. А. Martynyuk · Differential and Integral Equations · 1989

For the dynamical system x = f(t,x,P) describing perturbed motion under structural perturbations, a hierarchical matrix Lyapunov function is proposed which corresponds to a definite level of decomposition of the system.

Cited by 4Open access

The matrix sign function

Nataša Strabić, Vedran Šego · 2011

Dobro poznate funkcije (poput funkcije predznaka, korijena i logaritma) ponekad se, osim na brojevima, primjenjuju i na matricama. U clanku dajemo definicije takvih funkcija, te promatramo njihova osnovna svojstva. Zatim se bavimo matricnom funkcijom predznaka, koja je relativno jednostavna, ali i dovoljno složena da na njoj pokažemo kako se s takvim funkcijama radi. Na kraju opisujemo dva algoritma za racunanje vrijednosti opisane funkcije koje zainteresirani citatelj može prilagoditi i za racunanje druge funkcije.

Cited by 0

Function of a Matrix

Pierre-Yves Gaillard · viXra · 2013

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a.

Cited by 0Open access

The Matrix Sign Function

Peter Lancaster, Leiba Rodman · 1995

Abstract It has been shown in Chapter 7 that (under suitable hypotheses) the hermitian solutions of this Riccati equation are intimately connected to certain n dimensional invariant subspaces of M and, in particular, to the spectral sub space M+ of M corresponding to eigenvalues in the open right half-plane (see Theorem 7.6.2, for example).

Cited by 0

Matrix Biology: Extracellular Matrix – Building Function Through Complexity

Linda J. Sandell · 2015

The extracellular matrix (ECM) is the extracellular component of a multicellular organism or tissue that provides structural and biochemical support to the surrounding cells. The ECM functions to control many critical parameters of tissue homeostasis and response such as proliferation, apoptosis, development and morphogenesis. Characteristic of ECM is a complex interaction of specific large and small molecules that function as a composite structure: these structures can vary in different parts of the extracellular environment from a pericellular localization (concentrated around the cell) to interterritorial, making up the bulk of the ECM. These complex networks confer the functions of the ECM that are tissue specific; they are also dynamic, changing over time and developmental stage as well as in a response to injury or disease. ECM is also a storehouse for molecules that can be released at later times, including growth factors that bind to the charged glysocaminoglycan chains of proteoglycans such as fibroblast growth factors (FGFs) and growth factors that bind to protein domains, such as bone morphogenetic proteins (BMPs) and transforming growth factor beta superfamily members (TGFβs).

Cited by 0Open access

Function of a Matrix (pdf)

Pierre-Yves Gaillard · Figshare · 2013

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a. (This is a pdf file. Tex file: link below.)

Cited by 0Open access