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References

  • Amestoy, P.; Buttari, A.; Higham, N. J.; L’Excellent, J.-Y.; Mary, T. and Vieublé, B. (2024). Five-Precision GMRES-Based Iterative Refinement. SIAM Journal on Matrix Analysis and Applications 45, 529–552.
  • Demmel, J.; Hida, Y.; Kahan, W.; Li, X. S.; Mukherjee, S. and Riedy, E. J. (2006). Error Bounds from Extra-Precise Iterative Refinement. ACM Trans. Math. Soft. 13, 325–351.
  • Higham, N. J. (1996). Accuracy and Stability of Numerical Algorithms (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA); p. xxviii+688.
  • J.J.Dongarra; C.B.Moler and J.H.Wilkinson (1983). Improving the accuracy of computed eigenvalues and eigenvectors. SIAM Journal on Numerical Analysis 20, 23–45.
  • Kelley, C. T. (2022). Notebook for Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia, https://github.com/ctkelley/NotebookSIAMFANL. IJulia Notebook.
  • Kelley, C. T. (2022). SIAMFANLEquations.jl. Julia Package.
  • Kelley, C. T. (2022). Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia. No. 20 of Fundamentals of Algorithms (SIAM, Philadelphia).
  • Kelley, C. T. (2024). Interprecision transfers in iterative refinement, arXiv:2407.00827 [math.NA], submitted for publication.
  • Kelley, C. T. (2024). Using MultiPrecisionArrays.jl: Iterative Refinement in Julia, arXiv:2311.14616 [math.NA].
  • Kelley, C. T. (2024). MultiPrecisionArrays.jl. Julia Package.
  • Saad, Y. and Schultz, M. (1986). GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp. 7, 856–869.
  • der Vorst, H. A. (1992). Bi-CGSTAB: A fast and smoothly converging variant to Bi-CG for the solution of nonsymmetric systems. SIAM J. Sci. Stat. Comp. 13, 631–644.
  • Wilkinson, J. H. (1948). Progress Report on the Automatic Computing Engine. Technical Report MA/17/1024 (Mathematics Division, Department of Scientific and Industrial Research, National Physical Laboratory, Teddington, UK).