Kao, Mong-Jen Iterative partial rounding for vertex cover with hard capacities. (English) Zbl 07303843 Algorithmica 83, No. 1, 45-71 (2021). MSC: 68W 05C PDF BibTeX XML Cite \textit{M.-J. Kao}, Algorithmica 83, No. 1, 45--71 (2021; Zbl 07303843) Full Text: DOI
Blanchard, Pierre; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Pranesh, Srikara Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores. (English) Zbl 1452.65425 SIAM J. Sci. Comput. 42, No. 3, C124-C141 (2020). MSC: 65Y10 65F05 65F08 65G50 PDF BibTeX XML Cite \textit{P. Blanchard} et al., SIAM J. Sci. Comput. 42, No. 3, C124--C141 (2020; Zbl 1452.65425) Full Text: DOI
Paige, Christopher C. Accuracy of the Lanczos process for the eigenproblem and solution of equations. (English) Zbl 1427.65044 SIAM J. Matrix Anal. Appl. 40, No. 4, 1371-1398 (2019). MSC: 65F10 65F15 65F25 65F50 65G50 15A18 15B57 PDF BibTeX XML Cite \textit{C. C. Paige}, SIAM J. Matrix Anal. Appl. 40, No. 4, 1371--1398 (2019; Zbl 1427.65044) Full Text: DOI
Krishnaswamy, Ravishankar; Li, Shi; Sandeep, Sai Constant approximation for \(k\)-median and \(k\)-means with outliers via iterative rounding. (English) Zbl 1428.68393 Diakonikolas, Ilias (ed.) et al., Proceedings of the 50th annual ACM SIGACT symposium on theory of computing, STOC ’18, Los Angeles, CA, USA, June 25–29, 2018. New York, NY: Association for Computing Machinery (ACM). 646-659 (2018). MSC: 68W25 62H30 PDF BibTeX XML Cite \textit{R. Krishnaswamy} et al., in: Proceedings of the 50th annual ACM SIGACT symposium on theory of computing, STOC '18, Los Angeles, CA, USA, June 25--29, 2018. New York, NY: Association for Computing Machinery (ACM). 646--659 (2018; Zbl 1428.68393) Full Text: DOI
Calinescu, Gruia; Kortsarz, Guy; Nutov, Zeev Improved approximation algorithms for minimum power covering problems. (English) Zbl 07002068 Epstein, Leah (ed.) et al., Approximation and online algorithms. 16th international workshop, WAOA 2018, Helsinki, Finland, August 23–24, 2018. Revised selected papers. Cham: Springer (ISBN 978-3-030-04692-7/pbk; 978-3-030-04693-4/ebook). Lecture Notes in Computer Science 11312, 134-148 (2018). MSC: 68W25 68W27 PDF BibTeX XML Cite \textit{G. Calinescu} et al., Lect. Notes Comput. Sci. 11312, 134--148 (2018; Zbl 07002068) Full Text: DOI
Cools, Siegfried; Yetkin, Emrullah Fatih; Agullo, Emmanuel; Giraud, Luc; Vanroose, Wim Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined conjugate gradient method. (English) Zbl 1392.65048 SIAM J. Matrix Anal. Appl. 39, No. 1, 426-450 (2018). MSC: 65F10 65F50 65G50 65Y05 65Y20 PDF BibTeX XML Cite \textit{S. Cools} et al., SIAM J. Matrix Anal. Appl. 39, No. 1, 426--450 (2018; Zbl 1392.65048) Full Text: DOI arXiv
Carson, Erin; Higham, Nicholas J. Accelerating the solution of linear systems by iterative refinement in three precisions. (English) Zbl 1453.65067 SIAM J. Sci. Comput. 40, No. 2, A817-A847 (2018). MSC: 65F10 65F05 65F35 65G50 PDF BibTeX XML Cite \textit{E. Carson} and \textit{N. J. Higham}, SIAM J. Sci. Comput. 40, No. 2, A817--A847 (2018; Zbl 1453.65067) Full Text: DOI
Linhares, André; Swamy, Chaitanya Improved algorithms for MST and metric-TSP interdiction. (English) Zbl 1441.68290 Chatzigiannakis, Ioannis (ed.) et al., 44th international colloquium on automata, languages, and programming, ICALP 2017, Warsaw, Poland July 10–14, 2017. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 80, Article 32, 14 p. (2017). MSC: 68W25 90C27 90C35 PDF BibTeX XML Cite \textit{A. Linhares} and \textit{C. Swamy}, LIPIcs -- Leibniz Int. Proc. Inform. 80, Article 32, 14 p. (2017; Zbl 1441.68290) Full Text: DOI
Carson, Erin; Higham, Nicholas J. A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. (English) Zbl 1379.65019 SIAM J. Sci. Comput. 39, No. 6, A2834-A2856 (2017). MSC: 65F10 65F35 65G50 65F08 PDF BibTeX XML Cite \textit{E. Carson} and \textit{N. J. Higham}, SIAM J. Sci. Comput. 39, No. 6, A2834--A2856 (2017; Zbl 1379.65019) Full Text: DOI
Aihara, Kensuke Variants of the groupwise update strategy for short-recurrence Krylov subspace methods. (English) Zbl 1368.65046 Numer. Algorithms 75, No. 2, 397-412 (2017). MSC: 65F10 PDF BibTeX XML Cite \textit{K. Aihara}, Numer. Algorithms 75, No. 2, 397--412 (2017; Zbl 1368.65046) Full Text: DOI
Aurora, Pawan; Singh, Sumit; Mehta, Shashank K. Partial degree bounded edge packing problem for graphs and \(k\)-uniform hypergraphs. (English) Zbl 1354.90102 J. Comb. Optim. 32, No. 1, 159-173 (2016). MSC: 90C27 90C35 90C59 PDF BibTeX XML Cite \textit{P. Aurora} et al., J. Comb. Optim. 32, No. 1, 159--173 (2016; Zbl 1354.90102) Full Text: DOI
Adamczyk, Marek; Sviridenko, Maxim; Ward, Justin Submodular stochastic probing on matroids. (English) Zbl 1342.90112 Math. Oper. Res. 41, No. 3, 1022-1038 (2016). MSC: 90C15 68W25 90C27 PDF BibTeX XML Cite \textit{M. Adamczyk} et al., Math. Oper. Res. 41, No. 3, 1022--1038 (2016; Zbl 1342.90112) Full Text: DOI
Zhitnikov, V. P.; Sherykhalina, N. M.; Muksimova, R. R. Peculiarities of error accumulation in solving problems for simple equations of mathematical physics by finite difference methods. (Russian, English) Zbl 1349.65363 Sib. Zh. Vychisl. Mat. 19, No. 2, 139-152 (2016); translation in Numer. Analysis Appl. 9, No. 2, 107-117 (2016). MSC: 65M06 35K05 35L05 65M15 PDF BibTeX XML Cite \textit{V. P. Zhitnikov} et al., Sib. Zh. Vychisl. Mat. 19, No. 2, 139--152 (2016; Zbl 1349.65363); translation in Numer. Analysis Appl. 9, No. 2, 107--117 (2016) Full Text: DOI
Fukunaga, Takuro; Nutov, Zeev; Ravi, R. Iterative rounding approximation algorithms for degree-bounded node-connectivity network design. (English) Zbl 1322.05082 SIAM J. Comput. 44, No. 5, 1202-1229 (2015). MSC: 05C40 05C82 05C85 68Q25 68W25 68M10 PDF BibTeX XML Cite \textit{T. Fukunaga} et al., SIAM J. Comput. 44, No. 5, 1202--1229 (2015; Zbl 1322.05082) Full Text: DOI
Singh, Mohit; Lau, Lap Chi Approximating minimum bounded degree spanning trees to within one of optimal. (English) Zbl 1321.68507 J. ACM 62, No. 1, Article No. 1, 19 p. (2015). MSC: 68W25 05C85 68W40 90C35 PDF BibTeX XML Cite \textit{M. Singh} and \textit{L. C. Lau}, J. ACM 62, No. 1, Article No. 1, 19 p. (2015; Zbl 1321.68507) Full Text: DOI
Bai, Zhong-Zhi; Rozložník, Miroslav On the numerical behavior of matrix splitting iteration methods for solving linear systems. (English) Zbl 1317.65089 SIAM J. Numer. Anal. 53, No. 4, 1716-1737 (2015). MSC: 65F10 65F35 65G30 65G50 PDF BibTeX XML Cite \textit{Z.-Z. Bai} and \textit{M. Rozložník}, SIAM J. Numer. Anal. 53, No. 4, 1716--1737 (2015; Zbl 1317.65089) Full Text: DOI
Miyajima, Shinya A sharp error bound of the approximate solutions for saddle point linear systems. (English) Zbl 1302.65080 J. Comput. Appl. Math. 277, 36-46 (2015). MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{S. Miyajima}, J. Comput. Appl. Math. 277, 36--46 (2015; Zbl 1302.65080) Full Text: DOI
Adamczyk, Marek; Sviridenko, Maxim; Ward, Justin Submodular stochastic probing on matroids. (English) Zbl 1359.90111 Mayr, Ernst W. (ed.) et al., 31st international symposium on theoretical aspects of computer science, STACS’ 14, Lyon, France, March 5–8, 2014. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-65-1). LIPIcs – Leibniz International Proceedings in Informatics 25, 29-40 (2014). MSC: 90C27 68W25 90C15 90C59 PDF BibTeX XML Cite \textit{M. Adamczyk} et al., LIPIcs -- Leibniz Int. Proc. Inform. 25, 29--40 (2014; Zbl 1359.90111) Full Text: DOI
Deng, Shaohui; Wang, Guozhao Error estimations and applications of a new class of graphics fitting methods. (Chinese. English summary) Zbl 1313.65022 J. Zhejiang Univ., Eng. Sci. 45, No. 5, 942-947, 956 (2014). MSC: 65D10 65D17 PDF BibTeX XML Cite \textit{S. Deng} and \textit{G. Wang}, J. Zhejiang Univ., Eng. Sci. 45, No. 5, 942--947, 956 (2014; Zbl 1313.65022) Full Text: DOI
Cheriyan, Joseph; Végh, László A. Approximating minimum-cost \(k\)-node connected subgraphs via independence-free graphs. (English) Zbl 1303.05097 SIAM J. Comput. 43, No. 4, 1342-1362 (2014). MSC: 05C40 05C85 05C60 68W25 90C27 90C35 PDF BibTeX XML Cite \textit{J. Cheriyan} and \textit{L. A. Végh}, SIAM J. Comput. 43, No. 4, 1342--1362 (2014; Zbl 1303.05097) Full Text: DOI
Gergelits, Tomáš; Strakoš, Zdeněk Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations. (English) Zbl 1298.65054 Numer. Algorithms 65, No. 4, 759-782 (2014). MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{T. Gergelits} and \textit{Z. Strakoš}, Numer. Algorithms 65, No. 4, 759--782 (2014; Zbl 1298.65054) Full Text: DOI
Tu, Jian-hua; Du, Jun-feng; Yang, Feng-mei An iterative rounding 2-approximation algorithm for the \(k\)-partial vertex cover problem. (English) Zbl 1295.05241 Acta Math. Appl. Sin., Engl. Ser. 30, No. 2, 271-278 (2014). MSC: 05C85 05C70 68W25 90C27 PDF BibTeX XML Cite \textit{J.-h. Tu} et al., Acta Math. Appl. Sin., Engl. Ser. 30, No. 2, 271--278 (2014; Zbl 1295.05241) Full Text: DOI
Fazal, Qaisra; Neumaier, Arnold Error bounds for initial value problems by optimization. (English) Zbl 1327.65148 Soft Comput. 17, No. 8, 1345-1356 (2013). MSC: 65L70 65L05 34A34 65K05 90C26 65F08 PDF BibTeX XML Cite \textit{Q. Fazal} and \textit{A. Neumaier}, Soft Comput. 17, No. 8, 1345--1356 (2013; Zbl 1327.65148) Full Text: DOI
Aurora, Pawan; Singh, Sumit; Mehta, Shashank K. Partial degree bounded edge packing problem with arbitrary bounds. (English) Zbl 1303.68151 Fellows, Michael (ed.) et al., Frontiers in algorithmics and algorithmic aspects in information and management. Third joint international conference, FAW-AAIM 2013, Dalian, China, June 26–28, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-38755-5/pbk). Lecture Notes in Computer Science 7924, 24-35 (2013). MSC: 68W25 68W40 90C27 90C59 PDF BibTeX XML Cite \textit{P. Aurora} et al., Lect. Notes Comput. Sci. 7924, 24--35 (2013; Zbl 1303.68151) Full Text: DOI
Fukunaga, Takuro Approximating minimum cost source location problems with local vertex-connectivity demands. (English) Zbl 1280.68294 J. Discrete Algorithms 19, 30-38 (2013). MSC: 68W25 05C85 68R10 68M10 PDF BibTeX XML Cite \textit{T. Fukunaga}, J. Discrete Algorithms 19, 30--38 (2013; Zbl 1280.68294) Full Text: DOI
Kulisch, Ulrich Computer arithmetic and validity. Theory, implementation, and applications. 2nd revised and extended ed. (English) Zbl 1277.65028 de Gruyter Studies in Mathematics 33. Berlin: de Gruyter (ISBN 978-3-11-030173-1/hbk; 978-3-11-030179-3/ebook). xxii, 434 p. (2013). Reviewer: Svetoslav Markov (Sofia) MSC: 65G30 65G40 65G50 65G20 65D25 65H10 65F10 65-01 68W30 PDF BibTeX XML Cite \textit{U. Kulisch}, Computer arithmetic and validity. Theory, implementation, and applications. 2nd revised and extended ed. Berlin: de Gruyter (2013; Zbl 1277.65028) Full Text: DOI
Aazami, Ashkan; Cheriyan, Joseph; Laekhanukit, Bundit A bad example for the iterative rounding method for mincost \(k\)-connected spanning subgraphs. (English) Zbl 1258.90057 Discrete Optim. 10, No. 1, 25-41 (2013). MSC: 90C27 68W25 05C40 PDF BibTeX XML Cite \textit{A. Aazami} et al., Discrete Optim. 10, No. 1, 25--41 (2013; Zbl 1258.90057) Full Text: DOI
Rozložník, Miroslav; Tůma, Miroslav; Smoktunowicz, Alicja; Kopal, Jiří Numerical stability of orthogonalization methods with a non-standard inner product. (English) Zbl 1259.65069 BIT 52, No. 4, 1035-1058 (2012). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65F25 65F08 65F05 65G50 PDF BibTeX XML Cite \textit{M. Rozložník} et al., BIT 52, No. 4, 1035--1058 (2012; Zbl 1259.65069) Full Text: DOI
Fukunaga, Takuro; Nagamochi, Hiroshi Network design with weighted degree constraints. (English) Zbl 1241.90159 Discrete Optim. 7, No. 4, 246-255 (2010). MSC: 90C35 90C59 PDF BibTeX XML Cite \textit{T. Fukunaga} and \textit{H. Nagamochi}, Discrete Optim. 7, No. 4, 246--255 (2010; Zbl 1241.90159) Full Text: DOI
Fukunaga, Takuro; Nagamochi, Hiroshi Survivable network design problems with weighted degree constraints. (English) Zbl 1217.05212 RIMS Kôkyûroku Bessatsu B23, 49-62 (2010). MSC: 05C85 90C27 PDF BibTeX XML Cite \textit{T. Fukunaga} and \textit{H. Nagamochi}, RIMS Kôkyûroku Bessatsu B23, 49--62 (2010; Zbl 1217.05212)
Abe, Kuniyoshi; Sleijpen, Gerard L. G. BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices. (English) Zbl 1189.65058 J. Comput. Appl. Math. 234, No. 4, 985-994 (2010). MSC: 65F10 PDF BibTeX XML Cite \textit{K. Abe} and \textit{G. L. G. Sleijpen}, J. Comput. Appl. Math. 234, No. 4, 985--994 (2010; Zbl 1189.65058) Full Text: DOI
Jiránek, Pavel; Rozložník, Miroslav Adaptive version of simpler GMRES. (English) Zbl 1188.65033 Numer. Algorithms 53, No. 1, 93-112 (2010). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65G50 65F08 PDF BibTeX XML Cite \textit{P. Jiránek} and \textit{M. Rozložník}, Numer. Algorithms 53, No. 1, 93--112 (2010; Zbl 1188.65033) Full Text: DOI
Zhang, Zhenyue; He, Rui Error analysis of Padé iterations for computing matrix invariant subspaces. (English) Zbl 1183.65039 Front. Math. China 4, No. 2, 381-404 (2009). Reviewer: Constantin Popa (Constanţa) MSC: 65F15 65F10 65G50 PDF BibTeX XML Cite \textit{Z. Zhang} and \textit{R. He}, Front. Math. China 4, No. 2, 381--404 (2009; Zbl 1183.65039) Full Text: DOI
Zhang, Chi; Wang, Gang; Liu, Xiaoguang; Liu, Jing Approximating scheduling machines with capacity constraints. (English) Zbl 1248.90054 Deng, Xiaotie (ed.) et al., Frontiers in algorithmics. Third international workshop, FAW 2009, Hefei, China, June 20–23, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-02269-2/pbk). Lecture Notes in Computer Science 5598, 283-292 (2009). MSC: 90B35 68W25 PDF BibTeX XML Cite \textit{C. Zhang} et al., Lect. Notes Comput. Sci. 5598, 283--292 (2009; Zbl 1248.90054) Full Text: DOI
Pal, Srimanta Numerical methods. Principles, analysis and algorithms. (English) Zbl 1196.65001 Oxford: Oxford University Press (ISBN 978-0-19-569375-1/pbk). xii, 812 p. (2009). Reviewer: Georg Hebermehl (Berlin) MSC: 65-01 65Fxx 65Lxx 65Mxx 65Nxx 65Yxx 65D05 65D07 65D30 65G50 65H04 65H05 65H10 92B20 97M50 00A06 65C05 65R20 PDF BibTeX XML Cite \textit{S. Pal}, Numerical methods. Principles, analysis and algorithms. Oxford: Oxford University Press (2009; Zbl 1196.65001)
Kügler, Phillipp; Windsteiger, Wolfgang Algorithmic methods. Numbers, vectors, polynomials. (Algorithmische Methoden. Zahlen, Vektoren, Polynome.) (German) Zbl 1181.65001 Mathematik Kompakt. Basel: Birkhäuser (ISBN 978-3-7643-8434-0/pbk). xii, 160 p. (2009). Reviewer: Thomas Rauber (Bayreuth) MSC: 65-01 68-01 15-01 15-04 13-04 PDF BibTeX XML Cite \textit{P. Kügler} and \textit{W. Windsteiger}, Algorithmische Methoden. Zahlen, Vektoren, Polynome. Basel: Birkhäuser (2009; Zbl 1181.65001)
Jiránek, Pavel; Rozložník, Miroslav; Gutknecht, Martin H. How to make simpler GMRES and GCR more stable. (English) Zbl 1176.65036 SIAM J. Matrix Anal. Appl. 30, No. 4, 1483-1499 (2008). MSC: 65F10 65F35 65G50 PDF BibTeX XML Cite \textit{P. Jiránek} et al., SIAM J. Matrix Anal. Appl. 30, No. 4, 1483--1499 (2008; Zbl 1176.65036) Full Text: DOI
Jiránek, Pavel; Rozložník, Miroslav Maximum attainable accuracy of inexact saddle point solvers. (English) Zbl 1156.65029 SIAM J. Matrix Anal. Appl. 29, No. 4, 1297-1321 (2008). Reviewer: Dietrich Braess (Bochum) MSC: 65F10 65N22 65G50 PDF BibTeX XML Cite \textit{P. Jiránek} and \textit{M. Rozložník}, SIAM J. Matrix Anal. Appl. 29, No. 4, 1297--1321 (2008; Zbl 1156.65029) Full Text: DOI
Jiránek, Pavel; Rozložník, Miroslav Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems. (English) Zbl 1136.65037 J. Comput. Appl. Math. 215, No. 1, 28-37 (2008). MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{P. Jiránek} and \textit{M. Rozložník}, J. Comput. Appl. Math. 215, No. 1, 28--37 (2008; Zbl 1136.65037) Full Text: DOI
Singh, Mohit; Chi Lau, Lap Approximating minimum bounded degree spanning trees to within one of optimal. (English) Zbl 1232.68184 STOC’07. Proceedings of the 39th annual ACM symposium on theory of computing, San Diego, CA, USA, June 11–13, 2007. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-59593-631-8). 661-670 (2007). MSC: 68W25 68W40 05C85 PDF BibTeX XML Cite \textit{M. Singh} and \textit{L. Chi Lau}, in: Proceedings of the 39th annual ACM symposium on theory of computing, STOC 2007. San Diego, CA, USA, June 11--13, 2007. New York, NY: Association for Computing Machinery (ACM). 661--670 (2007; Zbl 1232.68184) Full Text: DOI
Petković, Miodrag S.; Milošević, Dušan M. The numerical stability of a Laguerre-like method for the simultaneous inclusion of polynomial zeros. (English) Zbl 1164.65407 Publ. Elektroteh. Fak., Univ. Beogr., Ser. Mat. 17, 93-109 (2006). Reviewer: Milan Kovačević (Niš) MSC: 65H05 65G30 30C15 65G50 PDF BibTeX XML Cite \textit{M. S. Petković} and \textit{D. M. Milošević}, Publ. Elektroteh. Fak., Univ. Beogr., Ser. Mat. 17, 93--109 (2006; Zbl 1164.65407) Full Text: DOI
Paige, Christopher C.; Rozlozník, Miroslav; Strakoš, Zdenek Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES. (English) Zbl 1113.65028 SIAM J. Matrix Anal. Appl. 28, No. 1, 264-284 (2006). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65F20 65F25 65F35 65F50 65G50 PDF BibTeX XML Cite \textit{C. C. Paige} et al., SIAM J. Matrix Anal. Appl. 28, No. 1, 264--284 (2006; Zbl 1113.65028) Full Text: DOI
Strakoš, Z.; Liesen, J. On numerical stability in large scale linear algebraic computations. (English) Zbl 1069.65030 ZAMM, Z. Angew. Math. Mech. 85, No. 5, 307-325 (2005). MSC: 65F10 65F15 65G20 65G50 PDF BibTeX XML Cite \textit{Z. Strakoš} and \textit{J. Liesen}, ZAMM, Z. Angew. Math. Mech. 85, No. 5, 307--325 (2005; Zbl 1069.65030) Full Text: DOI
van den Eshof, Jasper; Sleijpen, Gerard L. G. Inexact Krylov subspace methods for linear systems. (English) Zbl 1079.65036 SIAM J. Matrix Anal. Appl. 26, No. 1, 125-153 (2004). Reviewer: Petko Hr. Petkov (Sofia) MSC: 65F10 65G50 65F30 PDF BibTeX XML Cite \textit{J. van den Eshof} and \textit{G. L. G. Sleijpen}, SIAM J. Matrix Anal. Appl. 26, No. 1, 125--153 (2004; Zbl 1079.65036) Full Text: DOI
Cox, Lawrence H. On properties of multi-dimensional statistical tables. (English) Zbl 1021.62108 J. Stat. Plann. Inference 117, No. 2, 251-273 (2003). MSC: 62Q05 62H17 PDF BibTeX XML Cite \textit{L. H. Cox}, J. Stat. Plann. Inference 117, No. 2, 251--273 (2003; Zbl 1021.62108) Full Text: DOI
Cao, Zhi-Hao Rounding error analysis of two-stage iterative methods for large linear systems. (English) Zbl 1029.65026 Appl. Math. Comput. 139, No. 2-3, 371-381 (2003). Reviewer: Peter Reichensperger (Oberasbach) MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{Z.-H. Cao}, Appl. Math. Comput. 139, No. 2--3, 371--381 (2003; Zbl 1029.65026) Full Text: DOI
Strakoš, Zdeněk; Tichý, Petr On error estimation in the conjugate gradient method and why it works in finite precision computations. (English) Zbl 1026.65027 ETNA, Electron. Trans. Numer. Anal. 13, 56-80 (2002). Reviewer: F.Szidarovszky (Tucson) MSC: 65F10 65F25 65G50 PDF BibTeX XML Cite \textit{Z. Strakoš} and \textit{P. Tichý}, ETNA, Electron. Trans. Numer. Anal. 13, 56--80 (2002; Zbl 1026.65027) Full Text: EMIS EuDML
Liesen, J.; Rozlozník, M.; Strakos, Z. Least squares residuals and minimal residual methods. (English) Zbl 1012.65037 SIAM J. Sci. Comput. 23, No. 5, 1503-1525 (2002). Reviewer: Horst Hollatz (Magdeburg) MSC: 65F20 65F25 65F10 PDF BibTeX XML Cite \textit{J. Liesen} et al., SIAM J. Sci. Comput. 23, No. 5, 1503--1525 (2002; Zbl 1012.65037) Full Text: DOI
Davies, Philip I.; Higham, Nicholas J.; Tisseur, Françoise Analysis of the Cholesky method with iterative refinement for solving the symmetric definite generalized eigenproblem. (English) Zbl 1002.65044 SIAM J. Matrix Anal. Appl. 23, No. 2, 472-493 (2001). Reviewer: Liu Xinguo (Qingdao) MSC: 65F15 PDF BibTeX XML Cite \textit{P. I. Davies} et al., SIAM J. Matrix Anal. Appl. 23, No. 2, 472--493 (2001; Zbl 1002.65044) Full Text: DOI
Axelsson, O.; Barker, V. A. Finite element solution of boundary value problems. Theory and computation. Repr. (English) Zbl 0981.65130 Classics in Applied Mathematics. 35. Philadelphia, PA: SIAM. xxiii, 432 p. (2001). MSC: 65N30 65-02 65N15 65F05 65F10 35J25 35-04 PDF BibTeX XML Cite \textit{O. Axelsson} and \textit{V. A. Barker}, Finite element solution of boundary value problems. Theory and computation. Repr. Philadelphia, PA: SIAM (2001; Zbl 0981.65130) Full Text: DOI
Liang, Y.; Weston, J.; Szularz, M. Stability of polynomial preconditioning. (English) Zbl 1017.65043 Handlovicova, Angela (ed.) et al., Algoritmy 2000. Conference on scientific computing. Proceedings of contributed papers and posters. Vysoke Tatry, Podbanske, Slovakia, September 10-15, 2000. Bratislava: Slovenská Technická Univ. 264-272 (2001). MSC: 65F35 65F10 65F50 65Y05 PDF BibTeX XML Cite \textit{Y. Liang} et al., in: Algoritmy 2000. Conference on scientific computing. Proceedings of contributed papers and posters. Vysoke Tatry, Podbanske, Slovakia, September 10--15, 2000. Bratislava: Slovenská Technická Univ.. 264--272 (2001; Zbl 1017.65043)
Tisseur, Françoise Newton’s method in floating point arithmetic and iterative refinement of generalized eigenvalue problems. (English) Zbl 0982.65040 SIAM J. Matrix Anal. Appl. 22, No. 4, 1038-1057 (2001). Reviewer: Miloslav Znojil (Řež) MSC: 65F15 65F35 PDF BibTeX XML Cite \textit{F. Tisseur}, SIAM J. Matrix Anal. Appl. 22, No. 4, 1038--1057 (2001; Zbl 0982.65040) Full Text: DOI
Sleijpen, Gerard L. G.; Van der Vorst, Henk A.; Modersitzki, Jan Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems. (English) Zbl 0983.65046 SIAM J. Matrix Anal. Appl. 22, No. 3, 726-751 (2001). Reviewer: Krassimir Georgiev (Sofia) MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{G. L. G. Sleijpen} et al., SIAM J. Matrix Anal. Appl. 22, No. 3, 726--751 (2000; Zbl 0983.65046) Full Text: DOI
Argyros, Ioannis K. The effect of rounding errors on a certain class of iterative methods. (English) Zbl 0998.65061 Appl. Math. 27, No. 3, 369-375 (2000). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros}, Appl. Math. 27, No. 3, 369--375 (2000; Zbl 0998.65061) Full Text: DOI EuDML
Strakoš, Zdeněk Convergence and numerical behaviour of the Krylov space methods. (English) Zbl 0897.65023 Winter Althaus, G. (ed.) et al., Algorithms for large scale linear algebraic systems. Applications in science and engineering. Proceedings, Gran Canaria, Spain, June 23 - July 6, 1996. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 508, 175-196 (1998). MSC: 65F10 65D32 65D20 65F35 65G50 PDF BibTeX XML Cite \textit{Z. Strakoš}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 508, 175--196 (1998; Zbl 0897.65023)
Singer, Sanja Indefinite \(QR\) decomposition and applications. (Abstract of thesis). (English) Zbl 0890.65026 Glas. Mat., III. Ser. 32, No. 2, 347 (1997). MSC: 65F05 65F15 PDF BibTeX XML Cite \textit{S. Singer}, Glas. Mat., III. Ser. 32, No. 2, 347 (1997; Zbl 0890.65026)
Greenbaum, Anne Iterative methods for solving linear systems. (English) Zbl 0883.65022 Frontiers in Applied Mathematics. 17. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiv, 220 p. (1997). Reviewer: W.Gander (Zürich) MSC: 65F10 65-01 65F35 65N55 65G50 PDF BibTeX XML Cite \textit{A. Greenbaum}, Iterative methods for solving linear systems. Philadelphia, PA: SIAM (1997; Zbl 0883.65022)
Golub, Gene H. Matrix computation and the theory of moments. (English) Zbl 0865.65025 Bull. Belg. Math. Soc. - Simon Stevin Suppl., 1-9 (1996). Reviewer: H.Hollatz (Magdeburg) MSC: 65F30 44A60 65F10 41A55 42C05 65D32 PDF BibTeX XML Cite \textit{G. H. Golub}, Bull. Belg. Math. Soc. - Simon Stevin , 1--9 (1996; Zbl 0865.65025) Full Text: EuDML
Golub, Gene H. Matrix computation and the theory of moments. (English) Zbl 0839.65049 Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 1440-1448 (1995). MSC: 65F30 65D32 65F10 PDF BibTeX XML Cite \textit{G. H. Golub}, in: Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 1440--1448 (1995; Zbl 0839.65049)
Higham, Nicholas J.; Knight, Philip A. Matrix powers in finite precision arithmetic. (English) Zbl 0830.65022 SIAM J. Matrix Anal. Appl. 16, No. 2, 343-358 (1995). Reviewer: N.Köckler (Paderborn) MSC: 65F10 65G50 PDF BibTeX XML Cite \textit{N. J. Higham} and \textit{P. A. Knight}, SIAM J. Matrix Anal. Appl. 16, No. 2, 343--358 (1995; Zbl 0830.65022) Full Text: DOI
Christiansen, Søren; Hansen, Per Christian The effective condition number applied to error analysis of certain boundary collocation methods. (English) Zbl 0834.65033 J. Comput. Appl. Math. 54, No. 1, 15-36 (1994). Reviewer: O.Widlund (New York) MSC: 65F35 65N38 65F10 65G50 35J25 PDF BibTeX XML Cite \textit{S. Christiansen} and \textit{P. C. Hansen}, J. Comput. Appl. Math. 54, No. 1, 15--36 (1994; Zbl 0834.65033) Full Text: DOI
Atanassova, L. On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane. (English) Zbl 0807.65054 J. Comput. Appl. Math. 50, No. 1-3, 99-107 (1994). Reviewer: M.Marinov (Sofia) MSC: 65H05 65G30 30C15 65E05 PDF BibTeX XML Cite \textit{L. Atanassova}, J. Comput. Appl. Math. 50, No. 1--3, 99--107 (1994; Zbl 0807.65054) Full Text: DOI
Costea, Nicolae The statistic study of the rounding errors in iterative methods. (English) Zbl 0833.65039 An. Univ. “Ovidius” Constanţa, Ser. Mat. 1, 53-57 (1993). MSC: 65G50 65F10 PDF BibTeX XML Cite \textit{N. Costea}, An. Univ. ``Ovidius'' Constanţa, Ser. Mat. 1, 53--57 (1993; Zbl 0833.65039)
Notay, Yvan On the convergence rate of the conjugate gradients in presence of rounding errors. (English) Zbl 0791.65016 Numer. Math. 65, No. 3, 301-317 (1993). Reviewer: Yvan Notay (Bruxelles) MSC: 65F10 65F35 65G50 PDF BibTeX XML Cite \textit{Y. Notay}, Numer. Math. 65, No. 3, 301--317 (1993; Zbl 0791.65016) Full Text: DOI EuDML
Demmel, James W.; Higham, Nicholas J. Improved error bounds for undetermined system solvers. (English) Zbl 0770.65025 SIAM J. Matrix Anal. Appl. 14, No. 1, 1-14 (1993). Reviewer: M.Eiermann (Karlsruhe) MSC: 65F20 65F05 65F25 65G50 PDF BibTeX XML Cite \textit{J. W. Demmel} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 14, No. 1, 1--14 (1993; Zbl 0770.65025) Full Text: DOI
Donescu, Alexandru The noncommutative rings and iterative methods. (English) Zbl 0772.65019 Bul. Ştiinţ., Inst. Constr. Bucur. 35, No. 2, 71-74 (1992). MSC: 65F10 PDF BibTeX XML Cite \textit{A. Donescu}, Bul. Ştiinţ., Inst. Constr. Bucur. 35, No. 2, 71--74 (1992; Zbl 0772.65019)
Rump, S. M. On the solution of interval linear systems. (English) Zbl 0753.65030 Computing 47, No. 3-4, 337-353 (1992). Reviewer: H.Fischer (München) MSC: 65F10 65G30 PDF BibTeX XML Cite \textit{S. M. Rump}, Computing 47, No. 3--4, 337--353 (1992; Zbl 0753.65030) Full Text: DOI
Vigodner, A. M.; Pervozvanskij, A. A. A modification of the conjugate gradient algorithm for the stable solution of ill posed problems of the least squares method. (Russian) Zbl 0755.65041 Zh. Vychisl. Mat. Mat. Fiz. 31, No. 8, 1131-1145 (1991). Reviewer: Petko Hr.Petkov (Sofia) MSC: 65F20 65F10 PDF BibTeX XML Cite \textit{A. M. Vigodner} and \textit{A. A. Pervozvanskij}, Zh. Vychisl. Mat. Mat. Fiz. 31, No. 8, 1131--1145 (1991; Zbl 0755.65041)
Strakoš, Z. On the real convergence rate of the conjugate gradient method. (English) Zbl 0732.65021 Linear Algebra Appl. 154-156, 535-549 (1991). Reviewer: Z.Dostal (Ostrava) MSC: 65F10 PDF BibTeX XML Cite \textit{Z. Strakoš}, Linear Algebra Appl. 154--156, 535--549 (1991; Zbl 0732.65021) Full Text: DOI
Mikhlin, Solomon G. Error analysis in numerical processes. Transl. and rev. from the German. Transl. by Reinhard Lehmann. (English) Zbl 0786.65038 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts. Chichester: John Wiley & Sons Ltd. (ISBN 0-471-92133-5). 283 p. (1991). MSC: 65Gxx 65-02 65Fxx 65N15 65R20 74Sxx 65N22 PDF BibTeX XML Cite \textit{S. G. Mikhlin}, Error analysis in numerical processes. Transl. and rev. from the German. Transl. by Reinhard Lehmann. Chichester: John Wiley \&| Sons Ltd. (1991; Zbl 0786.65038)
Vigodner, A. M.; Pervozvanskij, A. A. A modification of the conjugate-gradient algorithm for the stable solution of an ill-conditioned problem by the method of least squares. (English. Russian original) Zbl 0785.65052 Comput. Math. Math. Phys. 31, No. 8, 6-17 (1991); translation from Zh. Vychisl. Mat. Mat. Fiz. 31, No. 8, 1131-1145 (1991). MSC: 65F20 65F10 PDF BibTeX XML Cite \textit{A. M. Vigodner} and \textit{A. A. Pervozvanskij}, Comput. Math. Math. Phys. 31, No. 8, 6--17 (1991; Zbl 0785.65052); translation from Zh. Vychisl. Mat. Mat. Fiz. 31, No. 8, 1131--1145 (1991)
Higham, N. J. How accurate is Gaussian elimination? (English) Zbl 0696.65020 Numerical analysis, Proc. 13th Biennial Conf., Dundee/UK 1989, Pitman Res. Notes Math. Ser. 228, 137-154 (1990). Reviewer: P.Reichensperger MSC: 65F05 65G50 PDF BibTeX XML
Frommer, Andreas Lösung linearer Gleichungssysteme auf Parallelrechnern. (Solution of systems of linear equations on parallel computers). (German) Zbl 0706.65014 Braunschweig: Friedr. Vieweg & Sohn. xvi, 267 p. DM 52.00 (1990). Reviewer: W.Schönauer MSC: 65F05 65F10 65Y05 65-02 65N22 PDF BibTeX XML Cite \textit{A. Frommer}, Lösung linearer Gleichungssysteme auf Parallelrechnern. (Solution of systems of linear equations on parallel computers). Braunschweig: Friedr. Vieweg \&| Sohn (1990; Zbl 0706.65014)
Ortega, James M. Numerical analysis: A second course. (English) Zbl 0701.65002 Classics in Applied Mathematics, 3. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiii, 201 p. $ 25.50 (1990). Reviewer: G.Mayer MSC: 65-02 65Fxx 65Hxx 65G50 65L10 PDF BibTeX XML Cite \textit{J. M. Ortega}, Numerical analysis: A second course. Philadelphia, PA: SIAM (1990; Zbl 0701.65002)
Kiełbasiński, A. Iterative refinement of least squares solutions computed from normal equations. (Polish. English summary) Zbl 0701.65028 Ann. Soc. Math. Pol., Ser. III, Mat. Stosow. 31, 91-101 (1989). Reviewer: Z.Dostal MSC: 65F20 65G50 PDF BibTeX XML Cite \textit{A. Kiełbasiński}, Ann. Soc. Math. Pol., Ser. III, Mat. Stosow. 31, 91--101 (1989; Zbl 0701.65028)
Abramchuk, V. S. Investigation of numerical stability of algorithms for solution of systems of linear equations. (Russian. English summary) Zbl 0693.65014 Dokl. Akad. Nauk Ukr. SSR, Ser. A 1989, No. 8, 3-5 (1989). Reviewer: F.Luban MSC: 65F05 65F10 65F20 PDF BibTeX XML Cite \textit{V. S. Abramchuk}, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1989, No. 8, 3--5 (1989; Zbl 0693.65014)
Petković, Miodrag S. On Halley-like algorithms for simultaneous approximation of polynomial complex zeros. (English) Zbl 0675.65039 SIAM J. Numer. Anal. 26, No. 3, 740-763 (1989). Reviewer: V.A.Kostova MSC: 65H05 30C15 PDF BibTeX XML Cite \textit{M. S. Petković}, SIAM J. Numer. Anal. 26, No. 3, 740--763 (1989; Zbl 0675.65039) Full Text: DOI
McNamee, J. M. A comparison of methods for terminating polynomial iterations. (English) Zbl 0661.65049 J. Comput. Appl. Math. 21, No. 2, 239-244 (1988). Reviewer: B.Döring MSC: 65H05 65G50 PDF BibTeX XML Cite \textit{J. M. McNamee}, J. Comput. Appl. Math. 21, No. 2, 239--244 (1988; Zbl 0661.65049) Full Text: DOI
Kiełbasiński, A.; Schwetlick, H. Numerische lineare Algebra. Eine computerorientierte Einführung. (German) Zbl 0635.65024 Mathematik für Naturwissenschaft und Technik, Bd. 18. Berlin: VEB Deutscher Verlag der Wissenschaften. 472 S. (1988). Reviewer: H.R.Schwarz MSC: 65Fxx 65-01 15-01 62J05 65C99 PDF BibTeX XML Cite \textit{A. Kiełbasiński} and \textit{H. Schwetlick}, Numerische lineare Algebra. Eine computerorientierte Einführung. Berlin (GDR): VEB Deutscher Verlag der Wissenschaften (1988; Zbl 0635.65024)
Duff, I.; Laminie, J.; Lichnewsky, A.; Thomasset, F. An experiment with arithmetic precision in linear algebra computations. (English) Zbl 0638.65035 Int. J. Numer. Methods Fluids 7, 1077-1092 (1987). Reviewer: H.Hollatz MSC: 65G50 65F05 65F10 PDF BibTeX XML Cite \textit{I. Duff} et al., Int. J. Numer. Methods Fluids 7, 1077--1092 (1987; Zbl 0638.65035) Full Text: DOI
Popa, Constantin Rounding error analysis of Jacobi and Gauss-Seidel iterative methods. (Romanian. English summary) Zbl 0623.65038 Stud. Cercet. Mat. 39, No. 3, 252-260 (1987). MSC: 65F10 65G50 65F35 PDF BibTeX XML Cite \textit{C. Popa}, Stud. Cercet. Mat. 39, No. 3, 252--260 (1987; Zbl 0623.65038)
Byers, Ralph Solving the algebraic Riccati equation with the matrix sign function. (English) Zbl 0611.65027 Linear Algebra Appl. 85, 267-279 (1987). Reviewer: S.Mirica MSC: 65F30 15A24 PDF BibTeX XML Cite \textit{R. Byers}, Linear Algebra Appl. 85, 267--279 (1987; Zbl 0611.65027) Full Text: DOI
Wilkinson, J. H. Error analysis revisited. (English) Zbl 0628.65035 Bull., Inst. Math. Appl. 22, 192-200 (1986). Reviewer: Petko Hr.Petkov MSC: 65G50 65F05 65F10 65-03 01A60 PDF BibTeX XML Cite \textit{J. H. Wilkinson}, Bull., Inst. Math. Appl. 22, 192--200 (1986; Zbl 0628.65035)
Robert, F. Machine iteration for a linear function. (English) Zbl 0626.65045 Comput. Math. Appl., Part B 12, 1259-1274 (1986). Reviewer: W.C.Rheinboldt MSC: 65H05 65G50 PDF BibTeX XML Cite \textit{F. Robert}, Comput. Math. Appl., Part B 12, 1259--1274 (1986; Zbl 0626.65045)
Rump, Siegfried M. New results on verified inclusions. (English) Zbl 0609.65033 Accurate scientific computations, Proc. Symp., Bad Neuenahr/FRG 1985, Lect. Notes Comput. Sci. 235, 31-69 (1986). Reviewer: E.Wagenführer MSC: 65G30 65F10 65H10 PDF BibTeX XML
Kulisch, Ulrich A new arithmetic for scientific computation. (English) Zbl 0609.65032 Accurate scientific computations, Proc. Symp., Bad Neuenahr/FRG 1985, Lect. Notes Comput. Sci. 235, 18-30 (1986). Reviewer: E.Wagenführer MSC: 65G30 65G50 65F05 65F10 PDF BibTeX XML
Jankowski, M.; Woźniakowski, H. The accurate solution of certain continuous problems using only single precision arithmetic. (English) Zbl 0623.65030 BIT 25, 635-651 (1985). Reviewer: F.Hofmann MSC: 65D32 65G50 65F10 PDF BibTeX XML Cite \textit{M. Jankowski} and \textit{H. Woźniakowski}, BIT 25, 635--651 (1985; Zbl 0623.65030) Full Text: DOI
Axelsson, O.; Barker, V. A. Finite element solution of boundary value problems. Theory and computation. (English) Zbl 0537.65072 Computer Science and Applied Mathematics. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XVIII, 432 p. $ 59.00 (1984). Reviewer: V.Arnautu MSC: 65N30 65-02 65N15 65F05 65F10 35J25 35-04 PDF BibTeX XML
Ypma, T. J. The effect of rounding errors on Newton-like methods. (English) Zbl 0519.65026 IMA J. Numer. Anal. 3, 109-118 (1983). MSC: 65H10 65G50 PDF BibTeX XML Cite \textit{T. J. Ypma}, IMA J. Numer. Anal. 3, 109--118 (1983; Zbl 0519.65026) Full Text: DOI
Linnainmaa, Seppo Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms. (English) Zbl 0515.65040 BIT 23, 346-359 (1983). MSC: 65G50 65G30 65F10 PDF BibTeX XML Cite \textit{S. Linnainmaa}, BIT 23, 346--359 (1983; Zbl 0515.65040) Full Text: DOI
Ursic, Silvio; Patarra, Cyro Exact solution of systems of linear equations with iterative methods. (English) Zbl 0502.65019 SIAM J. Algebraic Discrete Methods 4, 111-115 (1983). MSC: 65F10 PDF BibTeX XML Cite \textit{S. Ursic} and \textit{C. Patarra}, SIAM J. Algebraic Discrete Methods 4, 111--115 (1983; Zbl 0502.65019) Full Text: DOI
Rump, S. M. Computer und Rechengenauigkeit. (German) Zbl 0517.65023 Elektron. Rechenanlagen 24, 268-277 (1982). MSC: 65G50 65G30 65F10 PDF BibTeX XML Cite \textit{S. M. Rump}, Elektron. Rechenanlagen 24, 268--277 (1982; Zbl 0517.65023)
Axelsson, O.; Gustafsson, I. A preconditioned conjugate gradient method for finite element equations, which is stable for rounding errors. (English) Zbl 0442.65104 Information processing, Proc. IFIP Congr., Tokyo and Melbourne 1980, 723-728 (1980). MSC: 65N30 65F10 65F35 74S05 35J25 PDF BibTeX XML
Kershaw, David S. On the problem of unstable pivots in the incomplete LU-conjugate gradient method. (English) Zbl 0442.65022 J. Comput. Phys. 38, 114-123 (1980). MSC: 65F10 15A23 65G50 PDF BibTeX XML Cite \textit{D. S. Kershaw}, J. Comput. Phys. 38, 114--123 (1980; Zbl 0442.65022) Full Text: DOI
Wozniakowski, H. Roundoff-error analysis of a new class of conjugate-gradient algorithms. (English) Zbl 0431.65015 Linear Algebra Appl. 29, 507-529 (1980). MSC: 65F10 65G50 15B57 PDF BibTeX XML Cite \textit{H. Wozniakowski}, Linear Algebra Appl. 29, 507--529 (1980; Zbl 0431.65015) Full Text: DOI
Bollen, J. A. M. Round-off error analysis of the conjugate gradient algorithm. (English) Zbl 0413.65027 TH-Rep., Eindhoven WSK-6, 50 p. (1979). MSC: 65F10 65G50 65F35 PDF BibTeX XML
Miel, George J. Unified error analysis for Newton-type methods. (English) Zbl 0402.65038 Numer. Math. 33, 391-396 (1979). MSC: 65J15 47J25 65H10 PDF BibTeX XML Cite \textit{G. J. Miel}, Numer. Math. 33, 391--396 (1979; Zbl 0402.65038) Full Text: DOI EuDML