Abstract
The Lanczos methods studied in Chapter 8 have two shortcomings. First, they can suffer from breakdowns. Second, in each iteration we need to do a matrix-vector product with \(A^T\) (or \(A^*\)). In this chapter we study iterative methods, derived from those of Chapter 8, that do not need a multiplication with the transpose of A. They are sometimes called product-type or transpose-free methods. We consider, particularly, CGS and BiCGStab and their variants.
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Meurant, G., Duintjer Tebbens, J. (2020). Transpose-free Lanczos methods. In: Krylov Methods for Nonsymmetric Linear Systems. Springer Series in Computational Mathematics, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-030-55251-0_9
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DOI: https://doi.org/10.1007/978-3-030-55251-0_9
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Publisher Name: Springer, Cham
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