The Block Rational Arnoldi Method

The block version of the rational Arnoldi method is a widely used procedure for generating an orthonormal basis of a block rational Krylov space. We study block rational Arnoldi decompositions asso...

[1]  I. Elfadel,et al.  A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks , 1997, ICCAD 1997.

[2]  A. H. Bentbib,et al.  On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations , 2017 .

[3]  Khalide Jbilou,et al.  Block Krylov Subspace Methods for Solving Large Sylvester Equations , 2002, Numerical Algorithms.

[4]  Karen Willcox,et al.  Model reduction for active control design using multiple-point Arnoldi methods , 2003 .

[5]  Khalide Jbilou,et al.  An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems , 2016, J. Sci. Comput..

[6]  Mario Berljafa,et al.  Rational Krylov decompositions : theory and applications , 2017 .

[7]  Sebastian Birk,et al.  Deflated Shifted Block Krylov Subspace Methods for Hermitian Positive Definite Matrices , 2018 .

[8]  V. Simoncini,et al.  Preserving geometric properties of the exponential matrix by block Krylov subspace methods , 2006 .

[9]  Axel Ruhe.  Rational Krylov sequence methods for eigenvalue computation , 1984 .

[10]  M. Gutknecht,et al.  The block grade of a block Krylov space , 2009 .

[11]  Khalide Jbilou,et al.  The block Lanczos method for linear systems with multiple right-hand sides , 2004 .

[12]  Stefan Güttel,et al.  The nonlinear eigenvalue problem∗ , 2017 .

[13]  J. Cullum,et al.  A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices , 1974, CDC 1974.

[14]  R. Freund,et al.  Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm , 1997 .

[15]  Khalide Jbilou,et al.  Block Krylov Subspace Methods for Large Algebraic Riccati Equations , 2003, Numerical Algorithms.

[16]  Raf Vandebril,et al.  Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices , 2014 .

[17]  M. Heyouni,et al.  AN EXTENDED BLOCK ARNOLDI ALGORITHM FOR LARGE-SCALE SOLUTIONS OF THE CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATI ON ∗ , 2008 .

[18]  D. Szyld,et al.  Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM , 2020, SIAM J. Matrix Anal. Appl..

[19]  J. G. Lewis.  Algorithms for sparse matrix eigenvalue problems , 1977 .

[20]  M. Gutknecht,et al.  Block Krylov methods for Hermitian linear systems , 2004 .

[21]  Khalide Jbilou,et al.  Adaptive rational block Arnoldi methods for model reductions in large-scale MIMO dynamical systems , 2016 .

[22]  I. Gel'fand,et al.  Determinants of matrices over noncommutative rings , 1991 .

[23]  Raf Vandebril,et al.  On the Convergence of Rational Ritz Values , 2010, SIAM J. Matrix Anal. Appl..

[24]  G. W. Stewart,et al.  Matrix algorithms , 1998 .

[25]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[26]  Stefan Güttel,et al.  The RKFIT Algorithm for Nonlinear Rational Approximation , 2017, SIAM J. Sci. Comput..

[27]  Stefan Güttel,et al.  Generalized Rational Krylov Decompositions with an Application to Rational Approximation , 2015, SIAM J. Matrix Anal. Appl..

[28]  Henri Calandra,et al.  A Modified Block Flexible GMRES Method with Deflation at Each Iteration for the Solution of Non-Hermitian Linear Systems with Multiple Right-Hand Sides , 2013, SIAM J. Sci. Comput..

[29]  William E. Boyse,et al.  A Block QMR Method for Computing Multiple Simultaneous Solutions to Complex Symmetric Systems , 1996, SIAM J. Sci. Comput..

[30]  Gene H. Golub,et al.  The block Lanczos method for computing eigenvalues , 2007, Milestones in Matrix Computation.

[31]  George Cybenko.  Restrictions of Normal Operators, Padé Approximation and Autoregressive Time Series , 1984 .

[32]  H. Sadok,et al.  ALGEBRAIC PROPERTIES OF THE BLOCK GMRES AND BLOCK ARNOLDI METHODS , 2009 .

[33]  Heinrich Voss,et al.  Nonlinear Eigenvalue Problems , 2012 .

[34]  Lei Du,et al.  A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides , 2011, J. Comput. Appl. Math..

[35]  Henri Calandra,et al.  Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics , 2012, SIAM J. Sci. Comput..

[36]  Vladimir Puzyrev,et al.  A review of block Krylov subspace methods for multisource electromagnetic modelling , 2015 .

[37]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[38]  Stefan Güttel,et al.  A Rational Krylov Toolbox for MATLAB , 2014 .

[39]  R. Freund.  Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

[40]  Bo Zhang,et al.  A block rational Krylov method for 3-D time-domain marine controlled-source electromagnetic modelling , 2019, Geophysical Journal International.