bibtex

@techreport{kürschner2023inexact,      title={Inexact linear solves in the low-rank ADI iteration for large Sylvester equations},       author={Patrick Kürschner},      year={2023},      type={Arxiv eprint, 2312.02891},      url={https://arxiv.org/abs/2312.02891}}

@software{Kuersch_inexact_RKSM_ADI,  author = {K{\"u}rschner, P.},  title  = {Inexact RKSM and low-rank ADI for large Lyapunov equations (v1.0)},  year   = 2023,  doi    = {10.5281/zenodo.7461993}}
@software{Kuersch_RKSM_TLBT,  author = {K{\"u}rschner, P.},  title  = {RKSM_TLBT - Rational Krylov subspace methods for time-limited Gramians (v1.0)},  year   = 2022,  doi    = {10.5281/zenodo.7366026}
@article{polyBTD,   author =    {Vanderstukken, J. and K{\"u}rschner, P. and Domanov, I. and De Lathauwer, L.},  title =     {{S}ystems of polynomial equations, higher-order tensor decompositions and multidimensional harmonic retrieval: a unifying framework -- {P}art {II}:  {T}he block-term decomposition},  number =    {2},volume=42,  pages={913–953 },journal={SIAM J. Matrix Analysis and Applications},  year =     {2021},url={https://doi.org/10.1137/17M1150062},}

@Article{KueF20,  author =       {K{\"u}rschner, P. and Freitag, M.},  title =        {Inexact methods for the low rank solution to large scale {L}yapunov equations},  year =         2020,volume = 60,pages = {1221–1259},  journal = {BIT Numerical Mathematics},  url =          {https://doi.org/10.1007/s10543-020-00813-4}}
@article{AREcompare20, author =       {Benner, P. and Bujanovi{\'c}, Z. and K{\"u}rschner, P. and Saak, J.}, title = {A numerical comparison of solvers for large-scale, continuous-time algebraic {R}iccati equations and {LQR} problems}, journal =      {{SIAM} [J}. {S}ci. {C}omput.},  year = {2020}, volume = {42}, number=2, pages={A957--A996},doi = {10.1137/18M1220960}, url =         {https://doi.org/10.1137/18M1220960 },}
@software{AREsoftware20,  author       = {Saak, J. and K{\"u}rschner, P. and Bujanovi{\'c}, Z. and Benner, P.},  title        = {Collected MATLAB solvers for large-scale AREs},  year         = 2020,  publisher    = {Zenodo},  version      = {1.0},  doi          = {10.5281/zenodo.3662519},  url          = {https://doi.org/10.5281/zenodo.3662519}}
@article{Kuehn2020,author={Kuehn, Christianand K{\"u}rschner, Patrick},title={Combined error estimates for local fluctuations of {SPDE}s},journal={Advances in Computational Mathematics},year={2020},month={Feb},volume=46,number=1,pages=11,doi={10.1007/s10444-020-09766-2},}
@article{KreKM20,  author =       {Kressner, D. and K\"{u}rschner, P. and Massei, S.},  title =        {Low-rank updates and divide-and-conquer methods for quadratic matrix equations},  year =         2020,  journal =      {Numer. Alg.},  volume = 84,  doi =          {10.1007/s11075-019-00776-w},  pages = {717-741}
@article{KueDHetal19,  author =       {K{\"u}rschner, P. and Dolgov, S. and Harris, K.~D. and Benner P.},  title =        {Greedy low-rank algorithm for spatial connectome regression},  journal =      {J. Math. Neurosc. },  year =         {2019},volume =       {9},  number =       {1},pages = {9},  doi =          {10.1186/s13408-019-0077-0 }}


@Article{Kue19,  author = {K\"{u}rschner, P.},  title =  {Approximate residual minimizing shift parameters for the low-rank {ADI} iteration},    journal = {Electron. Trans. Numer. Anal.},  volume  = {51},  year    = {2019},  pages   = {240--261},  doi     = {10.1553/etna_vol51s240},
@arcticle{PalK21,   author= {Palitta, D. and K{\"u}rschner, P.},   title= {On the convergence of Krylov methods with low-rank truncations},  journal =      {Numer. Alg.},  year =         2021,  doi =          {10.1007/s11075-021-01080-2}}



@Article{PDufK20,   author= {{Pontes Duff}, I. and K{\"u}rschner, P.},   title= {Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems},journal = {Lin. Alg. Appl.},volume=623,pages={367-397},year ={2021},doi =  {10.1016/j.laa.2020.09.029}}

@Article{BenBKetal18b,  author =       {Benner, P. and Bujanovi{\'c}, Z. and K{\"u}rschner, P. and Saak, J.},  title =        {{RADI}: A low-rank {ADI}-type algorithm for large scale algebraic {R}iccati equations},  journal =      {Numer. Math.},  year =         2018,  volume =       138,  number =       2,  pages =        {301--330},  month =        feb,  doi =          {10.1007/s00211-017-0907-5}}
@Article{FreKP18,  author =       {Freitag, M. and K{\"u}rschner, P. and Pestana, J.},  title =        {{GMRES} convergence bounds for eigenvalue problems},  journal =      {Comput. Meth. Appl. Mat.},  year =         2018,  volume =       18,  number =       2,  pages =        {203--222},  month =        apr,  doi =          {10.1515/cmam-2017-0017}}
@Article{RedK18,  author =       {Redmann, M. and K{\"u}rschner, P.},  title =        {An Output Error Bound for Time-Limited Balanced Truncation},  journal =      {Syst. Control Lett.},  year =         2018,  volume =       121,  pages =        {1--6},  doi =          {10.1016/j.sysconle.2018.08.004}}
@Article{Kue18a,  author =       {K{\"u}rschner, P.},  title =        {Balanced truncation model order reduction in limited time intervals for large systems},  journal =      {Advances in Computational Mathematics},  volume =   {44},  number =  {6},  year =         2018,  pages =        {1821--1844},  doi =          {10.1007/s10444-018-9608-6}}
@PhdThesis{Kue16,  author =       {Patrick K{\"u}rschner},  title =        {Efficient Low-Rank Solution of Large-Scale Matrix Equations},  school =       OVGU,  year =         2016,  type =         {{D}issertation},  address =      {Magdeburg, Germany},  month =        apr,  note =         {Shaker Verlag, ISBN 978-3-8440-4385-3},  url =          {http://hdl.handle.net/11858/00-001M-0000-0029-CE18-2}}
@Article{BenKS16a,  author =       {P. Benner and P. K{\"u}rschner and J. Saak},  title =        {Frequency-Limited Balanced Truncation with Low-Rank Approximations},  journal =      {SIAM J. Sci. Comput.},  year =         2016,  volume =       38,  number =       1,  pages =        {A471--A499},  month =        Feb,  doi =          {10.1137/15M1030911}}
@Article{BenKTetal16,  author =       {Benner, P. and K{\"u}rschner, P. and Tomljanovi\'{c}, Z. and Truhar, N.},  title =        {Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm},  journal =      {ZAMM-Z. Angew. Math. Me.},  year =         2016,  volume =       96,  number =       5,  pages =        {604--619},  doi =          {10.1002/zamm.201400158}}
@Article{BenKS16,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {Low-Rank {Newton-ADI} methods for Large Nonsymmetric Algebraic {R}iccati Equations},  journal =      {J. Frankl. Inst.},  year =         2016,  volume =       353,  number =       5,  pages =        {1147--1167},  doi =          {10.1016/j.jfranklin.2015.04.016}}
@Article{FreK15,  author =       {Freitag, M.~A. and K{\"u}rschner, P.},  title =        {Tuned preconditioners for inexact two-sided inverse and {R}ayleigh quotient iteration},  journal =      {Numer. Linear Algebr.},  year =         2015,  volume =       22,  number =       1,  pages =        {175--196},  doi =          {10.1002/nla.1945},  issn =         {1099-1506}}
@Article{BenK14,  author =       {P. Benner and P. K{\"u}rschner},  title =        {Computing Real Low-rank Solutions of {S}ylvester equations by the Factored {ADI} Method},  journal =      {Computers and Mathematics with Applications},  year =         2014,  volume =       67,  number =       9,  pages =        {1656--1672},  doi =          {10.1016/j.camwa.2014.03.004},  issn =         {0898-1221}}
@Article{BenKS14b,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {Self-Generating and Efficient Shift Parameters in {ADI} Methods for Large {L}yapunov and {S}ylvester Equations},  journal =      {Electronic Transaction on Numerical Analysis},  year =         2014,  volume =       43,  pages =        {142--162},  issn =         {1068-9613}}
@Article{NowKEetal13,  author =       {Nowakowski, C. and K{\"u}rschner, P. and Eberhard, P. and Benner, P.},  title =        {Model reduction of an elastic crankshaft for elastic multibody simulations},  journal =      {ZAMM-Z. Angew. Math. Me.},  year =         2013,  volume =       93,  pages =        {198--216},  note =         {Available from                  \url{http://www.mpi-magdeburg.mpg.de/preprints/}},  publisher =    WileyVCH,  issn =         {1521-4001},  issue =        4,  doi =          {10.1002/zamm.201200054}}
@Article{BenKS13c,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {Efficient Handling of Complex Shift Parameters in the Low-Rank {C}holesky Factor {ADI} Method},  journal =      {Numer. Alg.},  year =         2013,  volume =       62,  number =       2,  pages =        {225--251},  doi =          {10.1007/s11075-012-9569-7},  issn =         {1017-1398}}
@Article{BenKS13a,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {A Reformulated Low-Rank {ADI} Iteration with Explicit Residual Factors},  journal =      {Proceedings in Applied Mathematics and Mechanics},  year =         2013,  volume =       13,  number =       1,  pages =        {585--586},  doi =          {10.1002/pamm.201310273},  issn =         {1617-7061}}
@InProceedings{FreK13,  author =       {Freitag, M.~A. and K{\"u}rschner, P.},  title =        {Inner-outer methods for large-scale two-sided eigenvalue problems},  booktitle =    {Oberwolfach Report - Numerical Solution of PDE Eigenvalue Problems},  year =         2013,  volume =       56,  pages =        {86--89},  doi =          {10.4171/OWR/2013/56}}
@Article{BenKS12b,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {A Goal-Oriented Dual {LRCF-ADI} for Balanced Truncation},  journal =      {IFAC Proceedings Volumes (7th Vienna International Conference on Mathematical Modelling)},  year =         2012,  volume =       45,  number =       2,  pages =        {752--757},  doi =          {10.3182/20120215-3-AT-3016.00133}}
@Article{BenKS12a,  author =       {Benner, P. and K{\"u}rschner, P. and Saak, J.},  title =        {Improved Second-Order Balanced Truncation for Symmetric Systems},  journal =      {IFAC Proceedings Volumes (7th Vienna International Conference on Mathematical Modelling)},  year =         2012,  volume =       45,  number =       2,  pages =        {758--762},  doi =          {10.3182/20120215-3-AT-3016.00134}}
@Article{BenKS13b,  author =       {P. Benner and P. K{\"u}rschner and J. Saak},  title =        {An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems},  journal =      {Mathematical and Computer Modelling of Dynamical Systems},  year =         2013,  volume =       19,  number =       6,  pages =        {593--615},  doi =          {10.1080/13873954.2013.794363}}
@Article{BenKS12c,  author =       {P. Benner and P. K{\"u}rschner and J. Saak},  title =        {Avoiding complex arithmetic in the low-rank {ADI} method efficiently},  journal =      {Proceedings in Applied Mathematics and Mechanics},  year =         2012,  volume =       12,  pages =        {639--640},  doi =          {10.1002/pamm.201210308},  issn =         {1617-7061},  publisher =    WileyVCH}
@TechReport{BenKS12d,  author =       {P. Benner and P. K{\"u}rschner and J. Saak},  title =        {Real versions of low-rank {ADI} methods with complex shifts},  institution =  {Max Planck Institute Magdeburg},  year =         2012,  type =         {Technical report},  number =       {MPIMD/12-11},  month =        may,  note =         {Available from                  \url{http://www.mpi-magdeburg.mpg.de/preprints/}}}
@Article{BenHK11a,  author =       {Benner, P. and Hochstenbach, M. and K{\"u}rschner, P.},  title =        {Two-sided harmonic subspace extractions for the generalized eigenvalue problem},  journal =      {Proceedings in Applied Mathematics and Mechanics},  year =         2011,  volume =       11,  pages =        {739--740},  date =         2011,  doi =          {10.1002/pamm.201110359},  issn =         {1617-7061},  publisher =    WileyVCH}
@InProceedings{BenHK11b,  author =       {Benner, P. and Hochstenbach, M.~E. and K{\"u}rschner, P.},  title =        {Model order reduction of large-scale dynamical systems with {J}acobi-{D}avidson style eigensolvers},  booktitle =    {International Conference on Communications, Computing and Control Applications (CCCA) 2011},  year =         2011,  pages =        {1--6},  month =        mar,  publisher =    {IEEE},  doi =          {10.1109/CCCA.2011.6031208}}
@InProceedings{BenEKetal11,  author =       {Benner, P. and Eberhard, P. and Knoll, G. and K{\"u}rschner, P. and Nowakowski, Christine C.and Ochse, G.},  title =        {Optimale {FE}-{R}eduktion, {M}oderne {M}odellreduktion elastischer {B}auteile f\"ur die {S}imulation flexibler                 {M}ehrk\"orpersysteme},  booktitle =    {Informationstagung Motoren: Fr\"uhjahrstagung 2011},  year =         2011,  volume =       {Heft R 553},  series =       {Forschungsvereinigung Verbrennungskraftmaschinen},  pages =        {175--197}}
@MastersThesis{Kue10,  author =       {P. K{\"u}rschner},  title =        {Two-Sided Eigenvalue Methods for Modal Approximation},  school =       {Chemnitz University of Technology, Department of Mathematics,                  Germany},  year =         2010}