Transpose-free multiple Lanczos and its application in Padé approximation
Journal of Computational and Applied Mathematics
Opendda: a Novel High-Performance Computational Framework for the Discrete Dipole Approximation
International Journal of High Performance Computing Applications
Transpose-free multiple Lanczos and its application in Padé approximation
Journal of Computational and Applied Mathematics
Bi-CGSTAB as an induced dimension reduction method
Applied Numerical Mathematics
Interpreting IDR as a Petrov-Galerkin Method
SIAM Journal on Scientific Computing
Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
SIAM Journal on Scientific Computing
A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
Algorithm 913: An elegant IDR(s) variant that efficiently exploits biorthogonality properties
ACM Transactions on Mathematical Software (TOMS)
Breakdown-free ML(k)BiCGStab algorithm for non-Hermitian linear systems
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
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We present a variant of the popular BiCGSTAB method for solving nonsymmetric linear systems. The method, which we denote by ML(k)BiCGSTAB, is derived from a variant of the BiCG method based on a Lanczos process using multiple (k 1) starting left Lanczos vectors. Compared with the original BiCGSTAB method, our new method produces a residual polynomial which is of lower degree after the same number of steps, but which also requires fewer matrix-vector products to generate, on average requiring only 1+1/k matvecs per step. Empirically, it also seems to be more stable and more quickly convergent. The new method can be implemented as a k-term recurrence and can be viewed as a bridge connecting the Arnoldi-based FOM/GMRES methods and the Lanczos-based BiCGSTAB methods.