Accurate eigenvalue decomposition of real symmetric arrowhead matrices and applications

[1]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[2]  S. B. Cavalcanti,et al.  Spontaneous emission and qubit transfer in spin-1/2 chains , 2010 .

[3]  I. Slapničar Symmetric Matrix Eigenvalue Techniques , 2007 .

[4]  Inderjit S. Dhillon,et al.  The design and implementation of the MRRR algorithm , 2006, TOMS.

[5]  Jack Dongarra,et al.  LAPACK Users' guide (third ed.) , 1999 .

[6]  James Demmel,et al.  LAPACK Users' Guide, Third Edition , 1999, Software, Environments and Tools.

[7]  Suely Oliveira A new parallel chasing algorithm for transforming arrowhead matrices to tridiagonal form , 1998, Math. Comput..

[8]  David E. Stewart,et al.  A graph-theoretic model of symmetric givens operations and its implications , 1997 .

[9]  A. Melman Numerical solution of a secular equation , 1995 .

[10]  Stanley C. Eisenstat,et al.  A Divide-and-Conquer Algorithm for the Bidiagonal SVD , 1995, SIAM J. Matrix Anal. Appl..

[11]  Stanley C. Eisenstat,et al.  A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem , 1995, SIAM J. Matrix Anal. Appl..

[12]  J. Barlow Error analysis of update methods for the symmetric eigenvalue problem , 1993 .

[13]  Carlos F. Borges,et al.  A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem , 1993 .

[14]  David Goldberg What Every Computer Scientist Should Know About Floating-Point Arithmetic , 1992 .

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

[16]  G. Stewart,et al.  Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices , 1990 .

[17]  Jack J. Dongarra,et al.  A fully parallel algorithm for the symmetric eigenvalue problem , 1985, PPSC.

[18]  J. W. Gadzuk Localized vibrational modes in Fermi liquids. General theory , 1981 .

[19]  B. Parlett The Symmetric Eigenvalue Problem , 1981 .

[20]  J. Cuppen A divide and conquer method for the symmetric tridiagonal eigenproblem , 1980 .

[21]  J. Bunch,et al.  Rank-one modification of the symmetric eigenproblem , 1978 .

[22]  Joshua Jortner,et al.  Intramolecular Radiationless Transitions , 1968 .

[23]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .