scholarly journals Comparative Performance Evaluation of an Accuracy-Enhancing Lyapunov Solver

Information ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 215
Author(s):  
Vasile Sima
Keyword(s):  
Correction Term ◽  
Lyapunov Equation ◽  
Computational Effort ◽  
Lyapunov Equations ◽  
Theory Analysis ◽  
Comparative Performance ◽  
Triangular Form ◽  
Analysis And Design ◽  
Technical Details ◽  
Dense Matrices

Lyapunov equations are key mathematical objects in systems theory, analysis and design of control systems, and in many applications, including balanced realization algorithms, procedures for reduced order models, Newton methods for algebraic Riccati equations, or stabilization algorithms. A new iterative accuracy-enhancing solver for both standard and generalized continuous- and discrete-time Lyapunov equations is proposed and investigated in this paper. The underlying algorithm and some technical details are summarized. At each iteration, the computed solution of a reduced Lyapunov equation serves as a correction term to refine the current solution of the initial equation. The best available algorithms for solving Lyapunov equations with dense matrices, employing the real Schur(-triangular) form of the coefficient matrices, are used. The reduction to Schur(-triangular) form has to be done only once, before starting the iterative process. The algorithm converges in very few iterations. The results obtained by solving series of numerically difficult examples derived from the SLICOT benchmark collections for Lyapunov equations are compared to the solutions returned by the MATLAB and SLICOT solvers. The new solver can be more accurate than these state-of-the-art solvers and requires little additional computational effort.

Screening for Cancer: Theory, Analysis, and Design.

1984 ◽  
Vol 79 (388) ◽  
pp. 959
Author(s):  
Neil Dubin ◽  
David M. Eddy
Keyword(s):  
Theory Analysis ◽  
Analysis And Design

scholarly journals Solution formulas for differential Sylvester and Lyapunov equations

CALCOLO ◽  
2019 ◽  
Vol 56 (4) ◽  
Author(s):  
Maximilian Behr ◽  
Peter Benner ◽  
Jan Heiland
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Applied Mathematics ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Spectral Theorem ◽  
Lyapunov Equations ◽  
Normal Operators ◽  
Symmetric Version ◽  
Induced Operator

AbstractThe differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction. The few available straight-forward numerical approaches when applied to large-scale systems come with prohibitively large storage requirements. This shortage motivates us to summarize and explore existing solution formulas for these equations. We develop a unifying approach based on the spectral theorem for normal operators like the Sylvester operator $${\mathcal {S}}(X)=AX+XB$$S(X)=AX+XB and derive a formula for its norm using an induced operator norm based on the spectrum of A and B. In view of numerical approximations, we propose an algorithm that identifies a suitable Krylov subspace using Taylor series and use a projection to approximate the solution. Numerical results for large-scale differential Lyapunov equations are presented in the last sections.

SOLVING DISCRETE-TIME LYAPUNOV EQUATIONS FOR THE CHOLESKY FACTOR ON A SHARED MEMORY MULTIPROCESSOR

1996 ◽  
Vol 06 (03) ◽  
pp. 365-376 ◽  
Author(s):  
JOSE M. CLAVER ◽  
VICENTE HERNANDEZ ◽  
ENRIQUE S. QUINTANA
Keyword(s):  
Parallel Algorithms ◽  
Shared Memory ◽  
Discrete Time ◽  
Lyapunov Equation ◽  
Lyapunov Equations ◽  
Parallel Solution ◽  
Cholesky Factor ◽  
Large Order ◽  
Shared Memory Multiprocessor

In this paper we study the parallel solution of the discrete-time Lyapunov equation. Two parallel fine and medium grain algorithms for solving dense and large order equations [Formula: see text] on a shared memory multiprocessor are presented. They are based on Hammarling’s method and directly obtain the Cholesky factor of the solution. The parallel algorithms work following an antidiagonal wavefront. In order to improve the performance, column-block-oriented and wrap-around algorithms are used. Finally, combined fine and medium grain parallel algorithms are presented.

Theory, analysis and design of high order reflective, absorptive filters

2017 ◽  
Vol 11 (6) ◽  
pp. 787-795 ◽  
Author(s):  
Senad Bulja ◽  
Andrei Grebennikov ◽  
Pawel Rulikowski
Keyword(s):  
High Order ◽  
Theory Analysis ◽  
Analysis And Design

A Weighted Three-Point-Based Strategy for Variance Estimation

2004 ◽  
Author(s):  
Thaweepat Buranathiti ◽  
Jian Cao ◽  
Wei Chen
Keyword(s):  
Variance Estimation ◽  
Order Approximation ◽  
Computational Effort ◽  
Normal Space ◽  
System Response ◽  
Test Problems ◽  
Deterministic Models ◽  
Analysis And Design ◽  
First Order ◽  
Input Variables

In manufacturing processes, it is widely accepted that uncertainty plays an important role and should be taken into account during analysis and design processes. However, uncertainty quantification of its effects on an end-product is a very challenging task, especially when an expensive computational effort is already needed in deterministic models such as sheet metal forming simulations. In this paper, we focus our work on the variance estimation of the system response. A weighted three-point-based strategy is proposed to efficiently and effectively estimate the variance of the system response. Three first-order derivatives for each variable are used to estimate the nonlinear behavior and variance of the system. The details of the derivation of the approach are presented in the paper. The optimal locations of the three points along each axis in the standard normal space and weights for input variables following normal distributions are proposed as (−1.8257,0.0,+1.8257) and (0.075,0.850,0.075), respectively. For input variables following uniform distributions U(−1,1), the optimal locations and weights are proposed as (−0.84517,0.0,+0.84517) and (0.04667,0.90666,0.04667), respectively. The proposed approach is applicable to nonlinear and multivariable systems as well as problems having no explicit function such as those design simulations based on finite element methods. The significant accuracy improvement over the traditional first-order approximation is demonstrated with a number of test problems. The proposed method requires significantly less computational effort compared with the Monte Carlo simulations. Discussions and conclusions of this work are given at the end of the paper.

Simulation of Digital Radio Mondiale (DRM) Coverage Prediction – A study case with Radio Republik Indonesia (RRI)

2017 ◽  
Vol 4 (1) ◽  
pp. 32-36
Author(s):  
Nabila Husna Shabrina
Keyword(s):  
Service Planning ◽  
Propagation Model ◽  
System Specification ◽  
Theory Analysis ◽  
Digital Radio ◽  
Analysis And Design ◽  
Transmitter Power ◽  
Antenna Type ◽  
Radio Systems ◽  
Coverage Prediction

In this paper, DRM is applied for simulating coverage prediction in Radio Republik Indonesia (RRI). The proposed method is developed by simulating high frequency propagation from RRI Pro 3 transmitter with VOACAP online software. The simulation is undertaken in some different conditions. The variation of antenna type and transmitter power are observed in the simulation. The time of propagation also discussed to predict the coverage. The result shows that the variation of parameter influences the coverage result of DRM propagation in HF band. Changing the antenna type and time of propagation will make impact in the range of coverage while adding power transmitter gives insignificantly effect to the range of coverage. Keywords—DRM, Prediction Coverage, VOACAP REFERENCES [1] ITU R-REP-BS.2144-2009-PDF-E, “Planning parameters and coverage for Digital Radio Mondiale (DRM) broadcasting at frequencies below 30 MHz”, 2009. [2] M. J. Bradley, “Digital Radio Mondiale: System and Receivers”,Roke Manor Research Ltd, UK, 2003 [3] G. Prieto, I. Pichel, D. Guerra, P. Angueira, J.M. Matias, J.L. Ordiales, A. Arrinda, “Digital Radio Mondiale: Broadcasting and Reception”, IEEE Press, 2004. [4] DRM Features, available under http://www.drm.org [5] “Digital Radio Mondiale (DRM); System Specification,” European Telecommunication Standards Institute (ETSI), ETSI TS 101980, 2001. [6] D. Setiawan, “Alokasi Frekuensi, Kebijakan dan Perencanaan Spektrum Indonesia”, Departemen Komunikasi dan Informatika, 2010. [7] P.A Bradley, Th Dambold, P.Suessmann, “Propagation model for HF Radio Service Planning”, HF Radio Systems and Techniques, Conference Publication No 474 0 IEE, 2000. [8] J.J. Carr, “Practical Antenna Handbook 4th Edition”, McGraw Hill, 1990. [9] J.M Matias et al, “DRM (Digital Radio Mondiale) Local Coverage Tests Using the 26 Mhz Broadcasting Band”, IEEE Transactions on Broadcasting, Vol. 53, No. 1, August 2007. [10] C. A. Balanis, “Antenna Theory Analysis and Design”, 2nd ed, John Wiley & Sons, 2005. [11] Keputusan Direktorat Jendral Pos dan Telekomunikasi Nomor 85/DIRJEN/1999, “Spesifikasi Teknis Perangkat Telekomunikasi, Persyaratan Teknis Perangkat Radio Siaran”, Jakarta, 1999.

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