The Block Rational Arnoldi Method
From MaRDI portal
Publication:5112234
DOI10.1137/19M1245505zbMath1441.65047OpenAlexW2924691308MaRDI QIDQ5112234
Stefan Güttel, Steven Elsworth
Publication date: 28 May 2020
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/19m1245505
Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Orthogonalization in numerical linear algebra (65F25)
Related Items (6)
On a family of low-rank algorithms for large-scale algebraic Riccati equations ⋮ An Efficient Block Rational Krylov Solver for Sylvester Equations with Adaptive Pole Selection ⋮ Inexact rational Krylov method for evolution equations ⋮ Low-Rank Updates of Matrix Functions II: Rational Krylov Methods ⋮ The extended symmetric block Lanczos method for matrix-valued Gauss-type quadrature rules ⋮ Divide-and-Conquer Methods for Functions of Matrices with Banded or Hierarchical Low-Rank Structure
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An adaptive rational block Lanczos-type algorithm for model reduction of large scale dynamical systems
- Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices
- A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides
- Rational Krylov sequence methods for eigenvalue computation
- An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation
- Preserving geometric properties of the exponential matrix by block Krylov subspace methods
- The block grade of a block Krylov space
- Algebraic properties of the block GMRES and block Arnoldi methods
- Rational Krylov algorithms for nonsymmetric eigenvalue problems. II: Matrix pairs
- The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices
- Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm
- Block Krylov subspace methods for large algebraic Riccati equations
- Krylov-subspace methods for reduced-order modeling in circuit simulation
- Quasideterminants
- Determinants of matrices over noncommutative rings
- The block Lanczos method for linear systems with multiple right-hand sides
- On some extended block Krylov based methods for large scale nonsymmetric Stein matrix equations
- Block Krylov subspace methods for functions of matrices
- The Quadratic Eigenvalue Problem
- Matrix Algorithms
- A Modified Block Flexible GMRES Method with Deflation at Each Iteration for the Solution of Non-Hermitian Linear Systems with Multiple Right-Hand Sides
- Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
- On the Convergence of Rational Ritz Values
- Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
- The nonlinear eigenvalue problem
- Restrictions of Normal Operators, Padé Approximation and Autoregressive Time Series
- Accuracy and Stability of Numerical Algorithms
- A Block QMR Method for Computing Multiple Simultaneous Solutions to Complex Symmetric Systems
- Generalized Rational Krylov Decompositions with an Application to Rational Approximation
- The RKFIT Algorithm for Nonlinear Rational Approximation
- Parallelization of the Rational Arnoldi Algorithm
- Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
- Block Krylov subspace methods for solving large Sylvester equations
This page was built for publication: The Block Rational Arnoldi Method