# Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners

## Abstract.

### Keywords

### MSC codes

## Get full access to this article

View all available purchase options and get full access to this article.

## References

*Iterative Solution Methods*, Cambridge University Press, Cambridge, UK, 1994.

*Numer. Math.*, 99 (2004), pp. 197–223.

*SIAM J. Numer. Anal.*, 45 (2007), pp. 1495–1516.

*Numer. Algorithms*, 50 (2009), pp. 297–380.

*Numer. Funct. Anal. Optim.*, 39 (2018), pp. 921–936.

*The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations*, Academic Press, New York, 1972.

*SIAM J. Numer. Anal.*, 39 (2001), pp. 300–329.

*Solvability of Discrete Helmholtz Equations*, https://doi.org/10.48550/arXiv.2105.02273, 2021.

*Modern Solvers for Helmholtz Problems*, Geosystems Mathematics, Birkhäuser/Springer, Cham, 2017, pp. 53–81.

*Numer. Linear Algebra Appl.*, 14, pp. 183–196.

*SIAM J. Numer. Anal.*, 23 (1986), pp. 44–57.

*SIAM J. Sci. Comput.*, 27 (2006), pp. 1471–1492.

*Modern Solvers for Helmholtz Problems*, Geosystems Mathematics, Birkhäuser/Springer, Cham, 2017, pp. 113–139.

*Theory and Practice of Finite Elements*, Appl. Math. Sci. 159, Springer-Verlag, New York, 2004.

*Numerical Analysis of Multiscale Problems*, I. G. Graham, T. Y. Hou, O. Lakkis, and R. Scheichl, eds., Lecture Notes in Comput. Sci. 83, Springer-Verlag, New York, 2012.

*Numerical Analysis of Multiscale Problems*, I. G. Graham, T. Y. Hou, O. Lakkis, and R. Scheichl, eds., Lecture Notes in Comput. Sci. 83, Springer-Verlag, New York, 2012.

*Adv. Appl. Math.*, 11 (1990), pp. 109–163.

*SIAM J. Sci. Comput.*, 24 (2002), pp. 38–60.

*Numer. Math.*, 131 (2015), pp. 567–614.

*SIAM J. Matrix Anal. Appl.*, 39 (2018), pp. 262–286.

*Eng. Anal. Bound. Elem.*, 57 (2015), pp. 66–71.

*Meshfree Methods for Partial Differential Equations VII*, Lect. Notes Comput. Sci. Eng. 100, Springer, Cham, 2015, pp. 145–162.

*SIAM J. Numer. Anal.*, 57 (2019), pp. 1369–1394.

*SIAM J. Numer. Anal.*, 58 (2020), pp. 2193–2211.

*SIAM J. Sci. Comput.*, 29 (2007), pp. 1942–1958.

*Classes of Linear Operators*, Vol. I, Oper. Theory Adv. Appl. 49, Birkhäuser Verlag, Basel, 1990.

*SIAM J. Numer. Anal.*, 30 (1993), pp. 343–376.

*Math. Comp.*, 86 (2017), pp. 2089–2127.

*Wave Motion*, 39 (2004), pp. 339–349.

*Contributions to the Solution of Systems of Linear Equations and the Determination of Eigenvalues*, O. Taussky, ed., Applied Mathematics Series 39, National Bureau of Standards, 1954, pp. 71–103.

*SIAM J. Numer. Anal.*, 53 (2015), pp. 1304–1324.

*Integral Equations Operator Theory*, 92 (2020), 14.

*Comput. Math. Appl.*, 46 (2003), pp. 1601–1610.

*SIAM Rev.*, 48 (2006), pp. 3–40.

*SIAM J. Sci. Comput.*, 20 (2000), pp. 1927–1949.

*Sloshing, Steklov and Corners: Asymptotics of Steklov Eigenvalues for Curvilinear Polygons*, https://arxiv.org/pdf/1908.06455.pdf, 2019.

*Numer. Math. Theory Methods Appl.*, 8 (2015), pp. 136–148.

*J. Comput. Acoust.*, 8 (2000), pp. 503–521.

*SIAM J. Sci. Comput.*, 25 (2004), pp. 1497–1515.

*SIAM Spotlights 1*, SIAM, Philadelphia, 2015.

*SIAM J. Numer. Anal.*, 27 (1990), pp. 656–694.

*SIAM J. Numer. Anal.*, 34 (1997), pp. 513–516.

*Functional Analysis*, Dover Publications, New York, 1990.

*Iterative Methods for Sparse Linear Systems*, 2nd ed., SIAM, Philadelphia, 2003.

*Computing*, 78 (2006), pp. 101–115.

*SIAM J. Optim.*, 24 (2014), pp. 435–466.

*SIAM Rev.*, 47 (2005), pp. 247–272.

*Math. Ann.*, 71 (1911), pp. 441–479.

*SIAM J. Numer. Anal.*, 17 (1980), pp. 14–17.

*SIAM J. Numer. Anal.*, 15 (1978), pp. 801–812.

## Information & Authors

### Information

#### Published In

#### Copyright

#### History

**Submitted**: 22 December 2021

**Accepted**: 22 November 2022

**Published online**: 27 April 2023

#### Keywords

#### MSC codes

#### Notes

### Authors

#### Funding Information

**Funding:**This research has been supported by the National Research, Development and Innovation Office (NKFIH), grants K137699 and SNN125119.

## Metrics & Citations

### Metrics

### Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

#### Cited By

There are no citations for this item

## View Options

### Get Access

**Access via your Institution**- Questions about how to access this content? Contact SIAM at
**[email protected]**.