Matrix analysis
ACM Transactions on Mathematical Software (TOMS)
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
SIAM Journal on Scientific Computing
QMRPACK: a package of QMR algorithms
ACM Transactions on Mathematical Software (TOMS)
A QL Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications
Using PLAPACK: parallel linear algebra package
Using PLAPACK: parallel linear algebra package
ScaLAPACK user's guide
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
A Jacobi--Davidson Method for Solving Complex Symmetric Eigenvalue Problems
SIAM Journal on Scientific Computing
Tridiagonalizing Complex Symmetric Matrices in Waveguide Simulations
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
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A non-splitting method for tridiagonalizing complex symmetric (non-Hermitian ) matrices is developed and analyzed. The main objective is to exploit the purely structural symmetry in terms of runtime performance. Based on the analytical derivation of the method, Fortran implementations of a blocked variant are developed and extensively evaluated experimentally. In particular, it is illustrated that a straightforward implementation based on the analytical derivation exhibits deficiencies in terms of numerical properties. Nevertheless, it is also shown that the blocked non-splitting method shows very promising results in terms of runtime performance. On average, a speed-up of more than three is achieved over competing methods. Although more work is needed to improve the numerical properties of the non-splitting tridiagonalization method, the runtime performance achieved with this non-unitary tridiagonalization process is very encouraging and indicates important research directions for this class of eigenproblems.