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2 Balancing-related model reduction methods (Q3384271)

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English	2 Balancing-related model reduction methods	scientific article

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scholarly article

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2 Balancing-related model reduction methods (English)

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zbMATH Open document ID

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10.1515/9783110498967-002

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System- and Data-Driven Methods and Algorithms

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publication date

15 December 2021

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

balanced truncation

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Gramians

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Lyapunov equations

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Lur'e equations

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differential-algebraic equations

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1515/9783110498967-002

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New model reduction scheme for bilinear systems

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Approximation of Large-Scale Dynamical Systems

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On the decay rate of Hankel singular values and related issues

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Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]

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Gramian-Based Model Reduction for Data-Sparse Systems

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Model reduction for systems with inhomogeneous initial conditions

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Model order reduction for linear and nonlinear systems: a system-theoretic perspective

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Low rank methods for a class of generalized Lyapunov equations and related issues

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Model Reduction and Approximation

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RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations

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Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems

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Positive operators and stable truncation

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Truncated Gramians for Bilinear Systems and Their Advantages in Model Order Reduction

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An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations

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Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems

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Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems

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An improved numerical method for balanced truncation for symmetric second-order systems

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Frequency-Limited Balanced Truncation with Low-Rank Approximations

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Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems

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Solving stable generalized Lyapunov equations with the matrix sign function

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Model reduction for stochastic systems

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Efficient balancing-based MOR for large-scale second-order systems

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Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey

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Model Order Reduction for Differential-Algebraic Equations: A Survey

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Numerical Solution of Algebraic Riccati Equations

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Dissipative systems analysis and control. Theory and applications

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Second-order balanced truncation

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Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems

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Realization and Structure Theory of Bilinear Dynamical Systems

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Direct methods and ADI‐preconditioned Krylov subspace methods for generalized Lyapunov equations

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A transformation approach to stochastic model reduction

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Model reduction of periodic systems: a lifting approach

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Internal positivity preserved model reduction

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On the structure of balanced and other principal representations of SISO systems

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On the cross-Gramian for symmetric MIMO systems

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Model reduction in limited time and frequency intervals

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All optimal Hankel-norm approximations of linear multivariable systems and their<i>L</i>,<sup>∞</sup>-error bounds†

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Realisation and Approximation of Linear Infinite-Dimensional Systems with Error Bounds

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State-space formulae for all stabilizing controllers that satisfy an \(H_{\infty}\)-norm bound and relations to risk sensitivity

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Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure

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On the nonuniqueness of singular value functions and balanced nonlinear realizations

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Balanced stochastic realizations

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A relative error bound for balanced stochastic truncation

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On the eigenvalue decay of solutions to operator Lyapunov equations

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A Survey of Model Reduction by Balanced Truncation and Some New Results

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Model Reduction by Balanced Truncation for Systems with Nuclear Hankel Operators

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Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation

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Balanced Averaging of Bilinear Systems with Applications to Stochastic Control

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Balanced truncation model reduction for systems with inhomogeneous initial conditions

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Balanced Truncation Model Reduction for a Class of Descriptor Systems with Application to the Oseen Equations

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An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation

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Cross-Gramian-Based Model Reduction: A Comparison

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An improved error estimate for reduced-order models of discrete-time systems

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Mathematical Systems Theory I

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Direct construction of minimal bilinear realizations from nonlinear input-output maps

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A new set of invariants for linear systems--Application to reduced order compensator design

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Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

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Differential-algebraic equations. A projector based analysis

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Balanced truncation model reduction for linear time-varying systems

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Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms

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Low Rank Solution of Lyapunov Equations

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A new subspace iteration method for the algebraic Riccati equation

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Model reduction of singular systems

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Singular perturbation approximation of balanced systems

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Analysis of an Iteration Method for the Algebraic Riccati Equation

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The ADI method for bounded real and positive real Lur'e equations

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Balancing and model reduction for second-order form linear systems

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Linear-quadratic Gaussian balancing for model reduction of differential-algebraic systems

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Natural Bilinear Control Processes

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Principal component analysis in linear systems: Controllability, observability, and model reduction

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Synthesis of minimum roundoff noise fixed point digital filters

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Balanced Parametrization of Classes of Linear Systems

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LQG balancing and reduced LQG compensation of symmetric passive systems†

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A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds

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Decay of Hankel singular values of analytic control systems

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A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations

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Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case

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Balanced realization and model reduction of singular systems

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Model reduction via balanced state space representations

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A Deflation Approach for Large-Scale Lur'e Equations

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A structure‐preserving doubling algorithm for Lur'e equations

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Type II Balanced Truncation for Deterministic Bilinear Control Systems

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Balancing transformations for infinite-dimensional systems with nuclear Hankel operator

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Balanced truncation model reduction of second-order systems

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Positive real and bounded real balancing for model reduction of descriptor systems

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Lyapunov Balancing for Passivity-Preserving Model Reduction of RC Circuits

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Positivity Preserving Balanced Truncation for Descriptor Systems

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Exploiting structure in large-scale electrical circuit and power system problems

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A Schur method for balanced-truncation model reduction

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Balanced Truncation of Linear Time-Varying Systems

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Balancing for nonlinear systems

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Reduced basis approximation of large scale parametric algebraic Riccati equations

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Linear time-variable systems: Balancing and model reduction

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Computational Methods for Linear Matrix Equations

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On two numerical methods for the solution of large-scale algebraic Riccati equations

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Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction

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The Sylvester equation and approximate balanced reduction

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On Criteria for Asymptotic Stability of Differential-Algebraic Equations

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Gramian-based model reduction for descriptor systems

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Balanced truncation model reduction for semidiscretized Stokes equation

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Low-rank iterative methods for projected generalized Lyapunov equations

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Krylov subspace methods for projected Lyapunov equations

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Periodic Lyapunov equations: Some applications and new algorithms

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Balancing related methods for minimal realization of periodic systems

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On generalized balanced realizations

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A new frequency-weighted balanced truncation method and an error bound

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A tighter relative-error bound for balanced stochastic truncation

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Dissipative dynamical systems. I: General theory

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Dissipative dynamical systems. II: Linear systems with quadratic supply rates

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Frequency-weighted ℒ/sub ∞/ norm and optimal Hankel norm model reduction

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Mathematics(1 entry)

mardi Publication:3384271

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