A new inclusion interval for the real eigenvalues of real matrices

Yinghua Wang; Xinnian Song; Lei Gao

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 979-992
  • ISSN: 0011-4642

Abstract

top
By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type B ¯ -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.

How to cite

top

Wang, Yinghua, Song, Xinnian, and Gao, Lei. "A new inclusion interval for the real eigenvalues of real matrices." Czechoslovak Mathematical Journal 73.3 (2023): 979-992. <http://eudml.org/doc/299100>.

@article{Wang2023,
abstract = {By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type $\overline\{\text\{B\}\}$-matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.},
author = {Wang, Yinghua, Song, Xinnian, Gao, Lei},
journal = {Czechoslovak Mathematical Journal},
keywords = {CKV-type B-matrix; P-matrix; real eigenvalues localization},
language = {eng},
number = {3},
pages = {979-992},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new inclusion interval for the real eigenvalues of real matrices},
url = {http://eudml.org/doc/299100},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Wang, Yinghua
AU - Song, Xinnian
AU - Gao, Lei
TI - A new inclusion interval for the real eigenvalues of real matrices
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 979
EP - 992
AB - By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type $\overline{\text{B}}$-matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness of the obtained results.
LA - eng
KW - CKV-type B-matrix; P-matrix; real eigenvalues localization
UR - http://eudml.org/doc/299100
ER -

References

top
  1. Brauer, A., 10.1215/S0012-7094-47-01403-8, Duke Math. J. 14 (1947), 21-26. (1947) Zbl0029.33701MR0020540DOI10.1215/S0012-7094-47-01403-8
  2. Cvetkovic, L., Kostic, V., Varga, R. S., A new Geršgorin-type eigenvalue inclusion set, ETNA, Electron. Trans. Numer. Anal. 18 (2004), 73-80. (2004) Zbl1069.15016MR2114449
  3. Chen, X., Xiang, S., 10.1007/s10107-005-0645-9, Math. Program. 106 (2006), 513-525. (2006) Zbl1134.90043MR2216793DOI10.1007/s10107-005-0645-9
  4. Wang, Y., Song, X., Gao, L., CKV-type-B-code, Available at https://github.com/gaolei11712/CKV-type-B-code.git. 
  5. Cvetković, D. L., Cvetković, L., Li, C., 10.1016/j.laa.2020.08.028, Linear Algebra Appl. 608 (2021), 158-184. (2021) Zbl1458.15064MR4142201DOI10.1016/j.laa.2020.08.028
  6. Fallat, S. M., Johnson, C. R., 10.1016/S0024-3795(98)10194-5, Linear Algebra Appl. 288 (1999), 149-173. (1999) Zbl0973.15013MR1670523DOI10.1016/S0024-3795(98)10194-5
  7. Fiedler, M., Pták, V., 10.21136/CMJ.1962.100526, Czech. Math. J. 12 (1962), 382-400. (1962) Zbl0131.24806MR0142565DOI10.21136/CMJ.1962.100526
  8. Gershgorin, S., Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR, Otd. Mat. Estest. Nauk, VII. Ser. 6 (1931), 749-754 Russian. (1931) Zbl0003.00102
  9. Li, H.-B., Huang, T.-Z., Li, H., 10.1002/nla.524, Numer. Linear Algebra Appl. 14 (2007), 391-405. (2007) Zbl1199.15072MR2312426DOI10.1002/nla.524
  10. Li, C., Li, Y., 10.1016/j.laa.2014.10.027, Linear Algebra Appl. 466 (2015), 343-356. (2015) Zbl1303.15034MR3278256DOI10.1016/j.laa.2014.10.027
  11. Li, C., Liu, Q., Li, Y., 10.1080/03081087.2014.986044, Linear Multilinear Algebra 63 (2015), 2159-2170. (2015) Zbl1335.15023MR3401934DOI10.1080/03081087.2014.986044
  12. Li, C., Wang, F., Zhao, J., Zhu, Y., Li, Y., 10.1016/j.cam.2013.04.022, J. Comput. Appl. Math. 255 (2014), 1-14. (2014) Zbl1291.15065MR3093400DOI10.1016/j.cam.2013.04.022
  13. Liu, J., Zhang, J., Liu, Y., 10.1016/j.laa.2012.02.001, Linear Algebra Appl. 437 (2012), 168-183. (2012) Zbl1248.15018MR2917437DOI10.1016/j.laa.2012.02.001
  14. Peña, J. M., 10.1137/S0895479800370342, SIAM J. Matrix Anal. Appl. 22 (2001), 1027-1037. (2001) Zbl0986.15015MR1824055DOI10.1137/S0895479800370342
  15. Peña, J. M., 10.1007/s00211-002-0427-8, Numer. Math. 95 (2003), 337-345. (2003) Zbl1032.15014MR2001081DOI10.1007/s00211-002-0427-8
  16. Peña, J. M., 10.1137/04061074X, SIAM J. Matrix Anal. Appl. 26 (2005), 908-917. (2005) Zbl1082.15031MR2178204DOI10.1137/04061074X
  17. Shen, S.-Q., Huang, T.-Z., Jing, Y.-F., 10.1137/080717961, SIAM J. Matrix Anal. Appl. 31 (2009), 816-830. (2009) Zbl1195.15023MR2530278DOI10.1137/080717961
  18. Song, X., Gao, L., 10.3934/math.2021630, AIMS Math. 6 (2021), 10846-10860. (2021) Zbl07536366MR4294618DOI10.3934/math.2021630
  19. Varga, R. S., Geršgorin-type eigenvalue inclusion theorems and their sharpness, ETNA, Electron. Trans. Numer. Anal. 12 (2001), 113-133. (2001) Zbl0979.15015MR1832018
  20. Varga, R. S., 10.1007/978-3-642-17798-9, Springer Series in Computational Mathematics 36. Springer, Berlin (2004). (2004) Zbl1057.15023MR2093409DOI10.1007/978-3-642-17798-9
  21. Zhao, J., Liu, Q., Li, C., Li, Y., 10.1016/j.laa.2018.04.028, Linear Algebra Appl. 552 (2018), 277-287. (2018) Zbl1391.15043MR3804489DOI10.1016/j.laa.2018.04.028

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.