Palindromic and Even Eigenvalue Problems - Analysis and Numerical Methods

[1]  Christian Mehl,et al.  Essential decomposition of polynomially normal matrices in real indefinite inner product spaces , 2006 .

[2]  David S. Watkins,et al.  The transmission of shifts and shift blurring in the QR algorithm , 1996 .

[3]  Peter Benner,et al.  Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils , 2002, SIAM J. Matrix Anal. Appl..

[4]  Roger A. Horn,et al.  Canonical forms for complex matrix congruence and ∗congruence , 2006, 0709.2473.

[5]  Daniel Kressner.  An Efficient and Reliable Implementation of the Periodic QZ Algorithm , 2001 .

[6]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[7]  Christian Mehl,et al.  On classification of normal matrices in indefinite inner product spaces , 2006 .

[8]  Adam W. Bojanczyk,et al.  Periodic Schur decomposition: algorithms and applications , 1992, Optics & Photonics.

[9]  Christian Mehl,et al.  Jacobi-like Algorithms for the Indefinite Generalized Hermitian Eigenvalue Problem , 2004, SIAM J. Matrix Anal. Appl..

[10]  R. Horn,et al.  Congruences of a square matrix and its transpose , 2004, 0709.2489.

[11]  Volker Mehrmann,et al.  Canonical forms for Hamiltonian and symplectic matrices and pencils , 1999 .

[12]  Leiba Rodman,et al.  Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence , 2005, SIAM Rev..

[13]  V. Mehrmann,et al.  On Hamiltonian and symplectic Hessenberg forms , 1991 .

[14]  A. Laub,et al.  Numerical solution of the discrete-time periodic Riccati equation , 1994, IEEE Trans. Autom. Control..

[15]  David S. Watkins.  ON THE REDUCTION OF A HAMILTONIAN MATRIX TO HAMILTONIAN SCHUR FORM , 2006 .

[16]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[17]  Volker Mehrmann,et al.  ON THE SOLUTION OF PALINDROMIC EIGENVALUE PROBLEMS , 2004 .

[18]  R. C. Thompson,et al.  Pencils of complex and real symmetric and skew matrices , 1991 .

[19]  Daniel Kressner,et al.  Numerical Methods for General and Structured Eigenvalue Problems , 2005, Lecture Notes in Computational Science and Engineering.

[20]  Roger A. Horn,et al.  A regularization algorithm for matrices of bilinear and sesquilinear forms , 2006 .

[21]  P. Dooren.  The Computation of Kronecker's Canonical Form of a Singular Pencil , 1979 .

[22]  Bo Kågström,et al.  Computing eigenspaces with specified eigenvalues of a regular matrix pair (A, B) and condition estimation: theory, algorithms and software , 1996, Numerical Algorithms.

[23]  P. Dooren,et al.  High performance algorithms for Toeplitz and block Toeplitz matrices , 1996 .

[24]  Karen S. Braman,et al.  The Multishift QR Algorithm. Part II: Aggressive Early Deflation , 2001, SIAM J. Matrix Anal. Appl..

[25]  V. Mehrmann,et al.  A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils , 1998 .

[26]  Rafael Mayo,et al.  Solving Dense Linear Systems on Graphics Processors , 2008, Euro-Par.

[27]  J. Dongarra,et al.  Exploiting the Performance of 32 bit Floating Point Arithmetic in Obtaining 64 bit Accuracy (Revisiting Iterative Refinement for Linear Systems) , 2006, ACM/IEEE SC 2006 Conference (SC'06).

[28]  Volker Mehrmann,et al.  Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations , 2006, SIAM J. Matrix Anal. Appl..

[29]  C. Loan,et al.  A Schur decomposition for Hamiltonian matrices , 1981 .

[30]  E. N. Antoniou,et al.  Linearizations of polynomial matrices with symmetries and their applications , 2006 .

[31]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[32]  Daniel Kressner,et al.  Structured Condition Numbers for Invariant Subspaces , 2006, SIAM J. Matrix Anal. Appl..

[33]  V. Mehrmann.  The Autonomous Linear Quadratic Control Problem , 1991 .

[34]  Vladimir V. Sergeichuk.  CLASSIFICATION PROBLEMS FOR SYSTEMS OF FORMS AND LINEAR MAPPINGS , 1988 .

[35]  A note on generalized Hessenberg matrices , 2005 .

[36]  Bo Kågström,et al.  Direct Eigenvalue Reordering in a Product of Matrices in Periodic Schur Form , 2006, SIAM J. Matrix Anal. Appl..

[37]  Paul Van Dooren,et al.  Computational methods for periodic systems - An overview , 2001 .

[38]  G. Stewart.  Updating a Rank-Revealing ULV Decomposition , 1993, SIAM J. Matrix Anal. Appl..

[39]  G. Golub,et al.  Linear least squares solutions by householder transformations , 1965 .

[40]  R. C. Thompson,et al.  The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil , 1976 .

[41]  P. Lancaster,et al.  Indefinite Linear Algebra and Applications , 2005 .

[42]  David S. Watkins,et al.  The matrix eigenvalue problem - GR and Krylov subspace methods , 2007 .

[43]  Daniel Kressner,et al.  Block algorithms for reordering standard and generalized Schur forms , 2006, TOMS.

[44]  V. Mehrmann,et al.  A new method for computing the stable invariant subspace of a real Hamiltonian matrix , 1997 .

[45]  Teiji Takagi,et al.  On an Algebraic Problem Reluted to an Analytic Theorem of Carathéodory and Fejér and on an Allied Theorem of Landau , 1924 .

[46]  R. Byers.  A Hamiltonian $QR$ Algorithm , 1986 .

[47]  David S. Watkins,et al.  Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem , 1994 .

[48]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[49]  C. Loan.  A Symplectic Method for Approximating All the Eigenvalues of a Hamiltonian Matrix , 1982 .

[50]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[51]  H. Faßbender.  Symplectic Methods for the Symplectic Eigenproblem , 2002, Springer US.

[52]  D. Kressner,et al.  Reordering the eigenvalues of a periodic matrix pair with applications in control , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[53]  Volker Mehrmann,et al.  Numerical methods for palindromic eigenvalue problems: Computing the anti‐triangular Schur form , 2009, Numer. Linear Algebra Appl..

[54]  John M. Lee,et al.  A Note on Canonical Forms for Matrix Congruence , 1996 .

[55]  Leiba Rodman,et al.  Bounded and stably bounded palindromic difference equations of first order , 2006 .

[56]  Stefano Grivet-Talocia,et al.  Passivity enforcement via perturbation of Hamiltonian matrices , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[57]  G. Stewart,et al.  An Algorithm for Generalized Matrix Eigenvalue Problems. , 1973 .

[58]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[59]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[60]  James Demmel,et al.  The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II: software and applications , 1993, TOMS.

[61]  W. Gragg,et al.  Singular value decompositions of complex symmetric matrices , 1988 .

[62]  Volker Mehrmann,et al.  A quaternion QR algorithm , 1989 .

[63]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[64]  J. Bunch.  The weak and strong stability of algorithms in numerical linear algebra , 1987 .

[65]  James Demmel,et al.  Jacobi's Method is More Accurate than QR , 1989, SIAM J. Matrix Anal. Appl..

[66]  B. Kågström,et al.  Computing periodic deflating subspaces associated with a specified set of eigenvalues , 2007 .

[67]  Jack J. Dongarra,et al.  The PlayStation 3 for High-Performance Scientific Computing , 2008, Computing in Science & Engineering.

[68]  Uwe Prells,et al.  CANONICAL STRUCTURES FOR PALINDROMIC MATRIX POLYNOMIALS , 2007 .

[69]  R. Byers,et al.  Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems , 2008 .

[70]  Rajni V. Patel.  On computing the eigenvalues of a symplectic pencil , 1993 .

[71]  Gerard L. G. Sleijpen,et al.  Jacobi-Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils , 1998, SIAM J. Sci. Comput..

[72]  Volker Mehrmann,et al.  A numerical method for computing the Hamiltonian Schur form , 2006, Numerische Mathematik.

[73]  B. Kågström,et al.  A Direct Method for Reordering Eigenvalues in the Generalized Real Schur form of a Regular Matrix Pair (A, B) , 1993 .

[74]  David S. Watkins,et al.  POLYNOMIAL EIGENVALUE PROBLEMS WITH HAMILTONIAN STRUCTURE , 2002 .

[75]  E. Chu,et al.  Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms , 2008 .

[76]  G. Stewart.  On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$ , 1972 .

[77]  C. Schröder.  A Structured Kronecker form for the Palindromic Eigenvalue Problem , 2006 .

[78]  V. Kublanovskaya.  On some algorithms for the solution of the complete eigenvalue problem , 1962 .