A two-directional Arnoldi process and its application to parametric model order reduction

DOI10.1016/j.cam.2008.05.059zbMath1160.65012OpenAlexW2169765983MaRDI QIDQ1008656

Yung-Ta Li, Yangfeng Su, Zhaojun Bai

Publication date: 30 March 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.059

zbMATH Keywords

numerical examplescomputational efficiencyArnoldi processKrylov subspacemodel order reductionorthonormal basesprojective techniquesorghogonalizationparameterized systems

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Complexity and performance of numerical algorithms (65Y20) Orthogonalization in numerical linear algebra (65F25)

Related Items (11)

Using Krylov-Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain ⋮ Robust stability of uncertain Markovian jump neural networks with mode-dependent time-varying delays and nonlinear perturbations ⋮ Model Order Reduction for Differential-Algebraic Equations: A Survey ⋮ Adaptive rational Krylov subspaces for large-scale dynamical systems ⋮ Model order reduction of parameterized circuit equations based on interpolation ⋮ Block Krylov subspace methods for the computation of structural response to turbulent wind ⋮ Parameter preserving model order reduction for MEMS applications ⋮ Parametric dominant pole algorithm for parametric model order reduction ⋮ Reduced‐order macromodeling of parameterized frequency responses ⋮ A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems ⋮ Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches

Uses Software

• MatrixMarket
• JDQR
• JDQZ
• CGS

Cites Work

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• Numerics of Gram-Schmidt orthogonalization
• Numerical behaviour of the modified Gram-Schmidt GMRES implementation
• Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
• Numerical stability of GMRES
• Structure-preserving model reduction using a Krylov subspace projection formulation
• Matrix Algorithms
• Implementation of the GMRES Method Using Householder Transformations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Stability analysis of 2-D systems
• Doubly-indexed dynamical systems: State-space models and structural properties
• Templates for the Solution of Algebraic Eigenvalue Problems
• Numerical Methods for Computing Angles Between Linear Subspaces
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems
• On stability robustness of 2-D systems described by the Fornasini-Marchesini model

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