Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System

1985 ◽  
pp. 16-28 ◽  
Author(s):  
M. A. Goberna ◽  
M. A. López
Keyword(s):  
Linear System ◽  
Characteristic Cone ◽  
Infinite Linear System ◽  
Infinite Linear

scholarly journals Matrix Transformations and Quasi-Newton Methods

2007 ◽  
Vol 2007 ◽  
pp. 1-17
Author(s):  
Boubakeur Benahmed ◽  
Bruno de Malafosse ◽  
Adnan Yassine
Keyword(s):  
Linear System ◽  
Newton Method ◽  
Matrix Transformations ◽  
Newton Methods ◽  
Tridiagonal Matrices ◽  
Finite Section ◽  
Finite Section Method ◽  
Quasi Newton ◽  
Infinite Linear System ◽  
Infinite Linear

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the formssξ,sξ∘,sξ(c), orlp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear system.

scholarly journals Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces

2020 ◽  
Vol 36 (36) ◽  
pp. 570-586 ◽  
Author(s):  
Fernando Pablos Romo ◽  
Víctor Cabezas Sánchez
Keyword(s):  
Linear System ◽  
Vector Spaces ◽  
Inner Product ◽  
Dimensional Vector ◽  
Product Spaces ◽  
Infinite Dimensional ◽  
Inner Product Spaces ◽  
Linear Maps ◽  
Infinite Linear System ◽  
Infinite Linear

The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in \text{Mat}_{n\times m} ({\mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, the least norm solution of an infinite linear system from the Moore-Penrose inverse offered is studied.

scholarly journals Discrete fragmentation systems in weighted $$\pmb {\ell ^{1}}$$ spaces

2020 ◽  
Vol 20 (4) ◽  
pp. 1419-1451
Author(s):  
Lyndsay Kerr ◽  
Wilson Lamb ◽  
Matthias Langer
Keyword(s):  
Steady State ◽  
Abstract Cauchy Problem ◽  
Initial Distribution ◽  
Analytic Solutions ◽  
Classical Solutions ◽  
Initial Cluster ◽  
Well Posed ◽  
Infinite Linear System ◽  
Infinite Linear

AbstractWe investigate an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters. We assume that each cluster is composed of identical units (monomers), and we allow mass to be lost, gained or conserved during each fragmentation event. By formulating the initial-value problem for the system as an abstract Cauchy problem (ACP), posed in an appropriate weighted $$\ell ^1$$ ℓ 1 space, and then applying perturbation results from the theory of operator semigroups, we prove the existence and uniqueness of physically relevant, classical solutions for a wide class of initial cluster distributions. Additionally, we establish that it is always possible to identify a weighted $$\ell ^1$$ ℓ 1 space on which the fragmentation semigroup is analytic, which immediately implies that the corresponding ACP is well posed for any initial distribution belonging to this particular space. We also investigate the asymptotic behaviour of solutions and show that, under appropriate restrictions on the fragmentation coefficients, solutions display the expected long-term behaviour of converging to a purely monomeric steady state. Moreover, when the fragmentation semigroup is analytic, solutions are shown to decay to this steady state at an explicitly defined exponential rate.

Many-Body-Systems and Exciton Model in New-Tamm-Dancoff- Formulation

1975 ◽  
Vol 30 (11) ◽  
pp. 1333-1346
Author(s):  
F. Wahl
Keyword(s):  
Many Body ◽  
Field Equations ◽  
Solid State Physics ◽  
Nonlinear Spinor ◽  
Exciton Model ◽  
Fundamental Field ◽  
Spinor Equation ◽  
Many Body Systems ◽  
Infinite Linear System ◽  
Infinite Linear

The NTD-method is a procedure to compute differences of eigenvalues in quantum mechanical problems: ωαβ=λα-λβ.It is an instruction to transform and truncate an infinite linear system of eigenvalue equations ω τk= Akm τm which is derived with the aid of fundamental field equations or corresponding Hamilton-operators, as e.g. with Heisenberg's nonlinear spinor equation. In this paper we want to test the NTD-method for a many-body-model in solid state physics. We elaborate on the physical and mathematical aspects by choosing a suitable transformation τ → φ = C τ to get a new linear 1 system ω φk= Bkk+2iφk+2i which permits a truncation to evaluate approximation of states. The efficiency of this method is demonstrated by treating a two-body-system in presence of polarisation quanta, known as exciton model

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Linear system reduction using approximate moment matching

1990 ◽  
Vol 137 (5) ◽  
pp. 322
Author(s):  
M. Bettayeb ◽  
U.M. Al-Saggaf
Keyword(s):  
Linear System ◽  
Moment Matching ◽  
System Reduction

Impossibility of steady squeezing for two-mode linear system without self-action

1991 ◽  
Vol 1 (9) ◽  
pp. 1217-1227 ◽  
Author(s):  
A. A. Bakasov ◽  
N. V. Bakasova ◽  
E. K. Bashkirov ◽  
V. Chmielowski
Keyword(s):  
Linear System
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