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S-SDD class of matrices and its application

S-SDD class of matrices and its application. Vladimir Kostić. University of Novi Sad Faculty of Science Dept. of Mathematics and Informatics. Introduction. Equivalent definitions of S-SDD matrices Bounds for the determinants Convergence area of PDAOR Subdirect sums. _. S. S.

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S-SDD class of matrices and its application

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  1. S-SDD class of matrices and its application Vladimir Kostić University of Novi Sad Faculty of Science Dept. of Mathematics and Informatics

  2. Introduction • Equivalent definitions of S-SDD matrices • Bounds for the determinants • Convergence area of PDAOR • Subdirect sums

  3. _ S S Equivalent definitions of S-SDD matrices L. Cvetkovic, V. Kostic and R. S. Varga, A new Gersgorin-type eigenvalue inclusion set, Electron. Trans. Numer. Anal., 18 (2004), 73–80

  4. Equivalent definitions of S-SDD matrices

  5. _ _ S S S S Equivalent definitions of S-SDD matrices

  6. H S-SDD SDD Equivalent definitions of S-SDD matrices

  7. Bounds for the determinants

  8. Bounds for the determinants

  9. Bounds for the determinants

  10. Bounds for the determinants

  11. Convergence of PDAOR A is block H-matrix iff M is an M-matrix A is block H-matrix iff M is an H-matrix

  12. Convergence of PDAOR

  13. Let be block SDD matrix. Then if we chose parameters in the following way: Convergence of PDAOR Lj.Cvetkovic, J. Obrovski, Some convergence results of PD relaxation methods, AMC 107 (2000) 103-112

  14. Convergence of PDAOR

  15. Convergence of PDAOR

  16. Let be block S-SDD matrix for set S. Then if we chose parameters in the following way: where Convergence of PDAOR Cvetković, Kostic,New subclasses of block H-matrices with applications to parallel decomposition-type relaxation methods, Numer. Alg. 42 (2006)

  17. Convergence of PDAOR

  18. Subdirect sums

  19. Subdirect sums Same sign pattern on the diagonal

  20. YES H SDD Subdirect sums NO A and B are , is the matrix C too?

  21. YES H S-SDD SDD Subdirect sums NO A and B are , is the matrix C too? R. Bru, F. Pedroche, and D. B. Szyld, Subdirect sums of S-Strictly Diagonally Dominant matrices, Electron. J. Linear Algebra, 15 (2006), 201–209

  22. Subdirect sums

  23. Subdirect sums

  24. Let IfAisS-SDD and B is SDD then is S-SDD. Subdirect sums R. Bru, F. Pedroche, and D. B. Szyld, Subdirect sums of S-Strictly Diagonally Dominant matrices, Electron. J. Linear Algebra, 15 (2006), 201–209

  25. Subdirect sums

  26. Subdirect sums of S-SDD matrices

  27. Subdirect sums of S-SDD matrices

  28. Let S be arbitrary IfAis- SDD, B is - SDD and then is S-SDD. Subdirect sums of S-SDD matrices

  29. Thank you for your attention

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