3 edition of **On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations** found in the catalog.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

- 70 Want to read
- 1 Currently reading

Published
**1989**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
.

Written in English

- Numerical analysis.

**Edition Notes**

Other titles | On Hilbert Schmidt norm convergence of Galerkin approximation for operator Riccati equations. |

Statement | I.G. Rosen. |

Series | ICASE report -- no. 88-71., NASA contractor report -- 181755., NASA contractor report -- NASA CR-181755. |

Contributions | Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL18034115M |

Then S is of Hilbert-Schmidt class. Moreover Q 1/2 TQ 1/2 e i = Re i, i N, so that R = Q 1/2 TQ 1/2 as required. We now prove a converse of Theorem 26 Chapter 1 Theorem Assume that there exists S L(H) symmetric and of Hilbert-Schmidt class such that R = Q 1/2 (1 S)Q 1/2. Then and are equivalent. Proof.5/5(1). Linear Algebra and its Applications Volume , Number , Janu E. Marques de Sá and Yu-Lin Zhang Ranks of submatrices and the off-diagonal indices of a square matrix E. Marques de Sá and Yu-Lin Zhang The number of Kronecker indices of square pencils of a special kind.

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ROSEN, On Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of infinite dimensional operator algebraic Riccati equations, in "Control and Estimation of Distributed Parameter Systems, Proceedings of the Fourth International Conference on the Control and Identification of Distributed Parameter Systems, Vorau Cited by: Get this from a library.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations. [I Gary Rosen; Langley Research Center.]. Convergence of Galerkin Approximations for Operator Riccati Equations-A Nonlinear Evolution Equation Approach I.

ROSEN* Department of Mathematics, University qf Southern Califarnia, Los Angeles, California, I Submitted by A. SchumitzkJ Received J We develop an approximation and convergence theory for Galerkin approxima. Approximation of the Algebraic Riccati Equation in the Hilbert Space of Hilbert–Schmidt Operators Article (PDF Available) in SIAM Journal on Control and Optimization 31(4) July with 23 Reads.

Abstract. The purpose of this article is to extend the representation theorem in [1] and [7] to certain classes of damped hyperbolic systems.

The original motivation for our study of hyperbolic systems comes from the work by Lupi, Chun, and Turner [8].Cited by: 6. ON HILBERT-SCHMIDT NORM CONVERGENCE OF GALERKIN APPROXIMATION FOR OPERATOR RICCATI EQUATIONS I. Rosen Department of Mathematics University of Southern California Los Angeles, CA ABSTRACT An abstract approximation framework for the solution of operator algebraic Riccati equations is developed.

ROSEN, “On Hilbert-Schmidt Norm Convergence of Galerkin Approximation for Operator Riccati Equations, King B.B. () Existence of Functional Gains for Parabolic Control Systems.

In: Computation and Control IV. Progress in Systems and Control Theory, vol Cited by: We develop an approximation and convergence theory for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators.

Operator norm and Hilbert Schmidt norm. Ask Question Asked 5 years, 6 months ago. Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers. Approximating a Hilbert-Schmidt operator. Boundedness of Volterra operator with Sobolev norm.

Recent theory of infinite dimensional Riccati equations is applied to the linear-quadratic optimal control problem for hereditary differential systems, and it is shown that, for most such problems, the operator solutions of the Riccati equations are of trace class (i.e., nuclear).Cited by: () Convergence of Galerkin approximations for operator Riccati equations—A nonlinear evolution equation approach.

Journal of Mathematical Analysis and Applications Cited by: Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. Deﬁnition. Operator A satisfying (∗) is called Hilbert-Schmidt. The class of such operators is denoted by S 2 and we introduce kAk S 2 = X j kAe jk2 1/2.

Remark 1. Any operator of ﬁnite rank is Hilbert-Schmidt. Remark 2. kAk S 2 introduced above satisﬁes all requirements of being a norm.

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations.

The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. Numerical Algorithms Volume 1, Number 2, Phillip J. Barry and Ronald N. Goldman Shape parameter deletion for Pólya curves M.

Barkatou Characterization of regular singular linear systems of difference equations J. Carnicer On best constrained interpolation. This is why we have chosen to adapt Lions’s Galerkin method to [] in Chapter 1. The application of this method to [] in Chapter 1 was presented in [HEN 04].

This Riccati equation was studied in the Hilbert–Schmidt framework in [HEN 08] making use of [TEM 71], that is, without referring to the factorization problem. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrodinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for.

Review of the first edition:‘The exposition is excellent and readable throughout, and should help bring the theory to a wider audience.' Daniel L.

Ocone Source: Stochastics and Stochastic Reports Review of the first edition:‘ a welcome contribution to the rather new area of infinite dimensional stochastic evolution equations, which is far from being complete, so it should provide both a Cited by: This self-contained monograph presents matrix algorithms and their analysis.

The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g. A general look at local principles with special emphasis on the norm computation aspect.

Integral Equations and Operator The (). Böttcher and B. Silbermann: Asymptotics of Toeplitz and Wiener-Hopf operators. In: Proc. 9th Conf. Probl. and Meth. in Math. Phys., Karl-Marx-Stadtpp.Teubner A. On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations.

NASA Technical Reports Server (NTRS) Rosen, I. G. An abstract approximation framework for the solution of operator algebraic Riccati equations is developed.- equations with the rational argument of the righthand side - linear equations - Bernoulli equations - Riccati equations - Equations x=f(y') a y=f(y') 4.

Existence theory for equations y'=f(x,y) - Peano theorem - Osgood theorem 5. Sensitivity on the righthand side and on the initial conditions 6. Linear n-th order differential equations 7.This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations.

The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.