Linear systems and robustness: a graph point of view

2007 ◽  
pp. 114-121 ◽  
Author(s):  
Tryphon T. Georgiou ◽  
Malcolm C. Smith
Keyword(s):  
Linear Systems ◽  
Point Of View

scholarly journals THE LINEAR SYSTEMS APPROACH TO LINEAR RATIONAL EXPECTATIONS MODELS

2017 ◽  
Vol 34 (3) ◽  
pp. 628-658 ◽  
Author(s):  
Majid M. Al-Sadoon
Keyword(s):  
Linear Systems ◽  
Representation Theorem ◽  
Existence And Uniqueness ◽  
Rational Expectations ◽  
Systems Approach ◽  
Point Of View

This paper considers linear rational expectations models from the linear systems point of view. Using a generalization of the Wiener-Hopf factorization, the linear systems approach is able to furnish very simple conditions for existence and uniqueness of both particular and generic linear rational expectations models. To illustrate the applicability of this approach, the paper characterizes the structure of stationary and cointegrated solutions, including a generalization of Granger’s representation theorem.

scholarly journals A Constructive Approach to Freyd Categories

2020 ◽  
Author(s):  
Sebastian Posur
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Computer Algebra ◽  
Point Of View ◽  
Standard Approach ◽  
Constructive Approach ◽  
Additive Category ◽  
Computational Structure ◽  
Alpha Beta ◽  
Finitely Presented

Abstract We discuss Peter Freyd’s universal way of equipping an additive category $$\mathbf {P}$$ P with cokernels from a constructive point of view. The so-called Freyd category $$\mathcal {A}(\mathbf {P})$$ A ( P ) is abelian if and only if $$\mathbf {P}$$ P has weak kernels. Moreover, $$\mathcal {A}(\mathbf {P})$$ A ( P ) has decidable equality for morphisms if and only if we have an algorithm for solving linear systems $$X \cdot \alpha = \beta $$ X · α = β for morphisms $$\alpha $$ α and $$\beta $$ β in $$\mathbf {P}$$ P . We give an example of an additive category with weak kernels and decidable equality for morphisms in which the question whether such a linear system admits a solution is computationally undecidable. Furthermore, we discuss an additional computational structure for $$\mathbf {P}$$ P that helps solving linear systems in $$\mathbf {P}$$ P and even in the iterated Freyd category construction $$\mathcal {A}( \mathcal {A}(\mathbf {P})^{\mathrm {op}} )$$ A ( A ( P ) op ) , which can be identified with the category of finitely presented covariant functors on $$\mathcal {A}(\mathbf {P})$$ A ( P ) . The upshot of this paper is a constructive approach to finitely presented functors that subsumes and enhances the standard approach to finitely presented modules in computer algebra.

ON LINEAR MULTI-INPUT SYSTEMS DEPENDING ON CONTINUOUS PARAMETERS. FEEDBACK EQUIVALENCES IN LOW DIMENSION

2012 ◽  
Vol 26 (25) ◽  
pp. 1246014
Author(s):  
M. V. CARRIEGOS ◽  
R. M. GARCÍA-FERNÁNDEZ ◽  
M. M. LÓPEZ-CABECEIRA ◽  
M. T. TROBAJO
Keyword(s):  
Linear Systems ◽  
Point Of View ◽  
Feedback Equivalence ◽  
Geometric Point ◽  
Low Dimension

We survey some recent results relating different notions of feedback equivalence of linear systems in a geometric point of view.

scholarly journals Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cui-Xia Li ◽  
Yan-Jun Liang ◽  
Shi-Liang Wu
Keyword(s):  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Point Of View ◽  
Subspace Methods ◽  
Practical Point ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From a practical point of view, we have analyzed and implemented inexact GPMHSS (IGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments are reported to confirm the efficiency of the proposed methods.

Identification of linear systems: A graph point of view

1992 ◽  
Author(s):  
Tryphon T. Georgiou ◽  
Craig R. Shankwitz ◽  
Malcolm C. Smith
Keyword(s):  
Linear Systems ◽  
Point Of View

scholarly journals A Double-Parameter GPMHSS Method for a Class of Complex Symmetric Linear Systems from Helmholtz Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Helmholtz Equation ◽  
Linear Systems ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Point Of View ◽  
Subspace Methods ◽  
Parameter Region ◽  
Practical Point ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Based on the preconditioned MHSS (PMHSS) and generalized PMHSS (GPMHSS) methods, a double-parameter GPMHSS (DGPMHSS) method for solving a class of complex symmetric linear systems from Helmholtz equation is presented. A parameter region of the convergence for DGPMHSS method is provided. From practical point of view, we have analyzed and implemented inexact DGPMHSS (IDGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical examples are reported to confirm the efficiency of the proposed methods.

scholarly journals On Osculating Systems of Differential Equations of Type (N, 1, 2)

1968 ◽  
Vol 31 ◽  
pp. 251-278 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Present Article ◽  
Point Of View ◽  
Main Subject ◽  
Systems Of Differential Equations ◽  
Projective Point

The main subject in the present article has the origin in the following quite primitive question: Linear systems of ordinary differential equations form a nice family. Then, from the projective point of view, what does correspond to linear systems?

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