CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Reduction to tridiagonal form and minimal realizations
SIAM Journal on Matrix Analysis and Applications
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Matrix computations (3rd ed.)
ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
SIAM Journal on Scientific Computing
A Lanczos-type method for multiple starting vectors
Mathematics of Computation
Computation of matrix-valued formally orthogonal polynomials and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
| Hi-index | 7.29 |
A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is mathematically equivalent to the two-sided methods without look-ahead or deflation steps, but avoids the use of the transpose of the system matrix. The method is applied to the computation of the matrix Padé approximation to a linear dynamical system. The result is a method which can be labeled transpose-free matrix Padé via Lanczos (TFMPVL). Under certain circumstances, TFMPVL will actually reduce the total number of matrix-vector products needed. It is illustrated with some numerical examples.