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MAT-TRIAD 2005 Three Days Full of Matrices Program and Abstracts MAT-TRIAD 2005 three days full of matrices B¦dlewo, Poland March 35, 2005 Program and abstracts Organizers • Stefan Banach International Mathematical Center, Warsaw • Faculty of Mathematics and Computer Science, Adam Mickiewicz Uni- versity, Pozna« • Institute of Socio-Economic Geography and Spatial Management, Faculty of Geography and Geology, Adam Mickiewicz University, Pozna« • Department of Mathematical and Statistical Methods, Agricultural Uni- versity, Pozna« edited by A. Markiewicz Department of Mathematical and Statistical Methods, Agricultural University, Pozna«, Poland and W. Woªy«ski Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Pozna«, Poland Contents Part I. Information Part II. Program Part III. Abstracts Some results on magic matrices ............................... 13 Marek Aleksiejczyk On linear combinations of idempotent matrices ............... 14 Jerzy K. Baksalary and Oskar Maria Baksalary Computing the stationary vector of Markov chains by Schwarz Iterations ..................................................... 15 Rafael Bru, Francisco Pedroche, and Daniel B. Szyld On the minimum rank for pattern matrices∗ .................. 16 Rafael Cantò and Beatriz Ricarte Projection methods for the linear split feasibility problems ... 17 Andrzej Cegielski Some subclasses of H-matrices and how to use them for eigen- value localization ............................................. 18 Ljiljana Cvetkovi¢ Matrix comparisons via eigenvector majorization: some re- sults ......................................................... 19 Pierre Druilhet Some observations on periodic matrices ....................... 20 Jürgen Groÿ Weighted symmetry and hermitancy of matrices .............. 21 Jan Hauke "When Leading Imply All" and other recent results .......... 22 Charles R. Johnson Structure preserving algorithms .............................. 23 Beata Laszkiewicz IV A regularization of large linear least squares problems via rank revealing Hauseholder postmultiplications .................... 24 Andrzej Ma¢kiewicz A robust approximate inverse preconditioner based on the Sherman-Morrison formula∗ .................................. 26 J. Cerdàn, J. Marìn, and J. Mas Norm estimates for eigenvalues of Riesz operators and matri- ces ........................................................... 28 Mieczysªaw Mastyªo Nonlinear polynomial eigenvalue problems with palindromic and symplectic structure ..................................... 29 Volker Mehrmann G-majorization and matrix inequalities ....................... 30 Marek Niezgoda Mixed prudential choice in matrix decision problem under uncertainty .................................................. 31 Tadeusz Ostrowski The conjugate gradients methods with indenite precondi- tioning ....................................................... 32 Miroslav Rozloºník Inverse eigenvalue problem for nonnegative matrices .......... 33 Helena migoc Structured matrices and ecient algorithms of polynomial in- terpolation ................................................... 34 Alicja Smoktunowicz, Iwona Wróbel, and Przemysªaw Kosowski Issai Schur (18751941) and the early development of the Schur complement: photographs, documents and biographi- cal remarks ................................................... 35 George P. H. Styan Characterizing the set of doubly stochastic matrices having unitary preimages ............................................ 36 Wojciech Tadej MINRES residual norms of diagonally translated linear systems 37 Jurjen Duintjer Tebbens Corollary 6 Route 66 to the structure of square matrices .. 39 Götz Trenkler V Augmented systems in the potential uid ow problem ....... 40 Miroslav T·ma On some uses of Sylvester-type equations ..................... 42 Kresimir Veselic Some properties of equiradial and equimodular sets .......... 43 Dominika Wojtera-Tyrakowska Part IV. List of Participants Index ......................................................... 53 Part I Information 3 The workshop will be held on 3-5 March 2005 at B¦dlewo (about 30 km from Pozna«). B¦dlewo is the Mathematical Research and Conference Center of the Polish Academy of Sciences - the setting is similar to Oberwolfach, with accommodation on site (for further info about this place please visit www.impan.gov.pl/Bedlewo). The aim of the workshop is to bring together researchers sharing an interest in a variety of aspects of matrix analysis and its applications and oer them a possibility to discuss current developments in these subjects. The format of this meeting will involve plenary talks and discussion sessions. Organizers • Stefan Banach International Mathematical Center, Warsaw • Faculty of Mathematics and Computer Science, Adam Mickiewicz Uni- versity, Pozna« • Institute of Socio-Economic Geography and Spatial Management, Faculty of Geography and Geology, Adam Mickiewicz University, Pozna« • Department of Mathematical and Statistical Methods, Agricultural Uni- versity, Pozna« Organizing committee: • Jan Hauke, Institute of Socio-Economic Geography and Spatial Manage- ment, Faculty of Geography and Geology, Adam Mickiewicz University, Pozna«, • Augustyn Markiewicz (chair), Department of Mathematical and Statisti- cal Methods, Agricultural University, Pozna«, • Tomasz Szulc, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Pozna«, • Waldemar Woªy«ski, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Pozna«. Part II Program Program Thursday, March 3, 2005 8:009:00 Breakfast Session I Chair C.R. Johnson 9:009:45 G.P.H. Styan: Issai Schur (18751941) and the early development of the Schur complement: photographs, documents and biograph- ical remarks 9:4510:30 G. Trenkler: Corollary 6 Route 66 to the structure of square matrices 10:3011:00 Coee break Session II Chair T. Szulc 11:0011:45 M. Mastyªo: Norm estimates for eigenvalues of Riesz operators and matrices 11:4512:30 R. Cantò: On the minimum rank for pattern matrices 13:0015:00 Lunch Session III Chair G. Trenkler 15:0015:45 O.M. Baksalary: On linear combinations of idempotent matrices 15:4516:30 P. Druilhet: Matrix comparisons via eigenvector majorization: some results 16:3017:00 Coee break Session IV Chair M. Mastyªo 17:0017:30 J. Mas: A robust approximate inverse preconditioner based on the Sherman-Morrison formula 17:3018:00 J. Hauke: Weighted symmetry and hermitancy of matrices 18:0018:30 T. Ostrowski: Mixed prudential choice in matrix decision problem under uncertainty 19:00 Dinner 8 Friday, March 4, 2005 8:009:00 Breakfast Session V Chair K. Veselic 9:009:45 C.R. Johnson: "When Leading Imply All" and other recent results 9:4510:30 H. Smigoc: Inverse eigenvalue problem for nonnegative matrices 10:3011:00 Coee break Session VI Chair M. Tuma 11:0011:45 L. Cvetkovi¢: Some subclasses of H-matrices and how to use them for eigenvalue localization 11:4512:30 R. Bru: Computing the stationary vector of Markov chains by Schwarz Iterations 13:0015:00 Lunch Session VII Chair L. Cvetkovi¢ 15:0015:45 M. T·ma: Augmented systems in the potential uid ow problem 15:4516:30 J.D. Tebbens: MINRES residual norms of diagonally translated linear systems 16:3017:00 Coee break Session VIII Chair K. Zi¦tak 17:0017:30 A. Smoktunowicz and I. Wróbel: Structured matrices and ecient algorithms of polynomial interpolation 17:3018:00 B. Laszkiewicz: Structure preserving algorithms 18:0018:30 D. Wojtera-Tyrakowska: Some properties of equiradial and equimodular sets 19:00 Dinner 9 Saturday, March 5, 2005 8:009:00 Breakfast Session IX Chair R. Bru 9:009:45 V. Mehrmann: Nonlinear polynomial eigenvalue problems with palindromic and symplectic structure 9:4510:30 M. Rozloºník: The conjugate gradients methods with indenite preconditioning 10:3011:00 Coee break Session X Chair V. Mehrmann 11:0011:45 K. Veselic: On some uses of Sylvester-type equations 11:4512:30 A. Ma¢kiewicz: A regularization of large linear least squares prob- lems via rank revealing Hauseholder postmultiplications 13:0015:00 Lunch Session XI Chair G.P.H. Styan 15:0015:45 J. Groÿ: Some observations on periodic matrices 15:4516:30 M. Niezgoda: G-majorization and matrix inequalities 16:3017:00 Coee break Session XII Chair J. Mas 17:0017:30 M. Aleksiejczyk: Some results on magic matrices 17:3018:00 W. Tadej: Characterizing the set of doubly stochastic matrices having unitary preimages 18:0018:30 A. Cegielski: Projection methods for the linear split feasibility problems 19:00 Dinner Part III Abstracts Marek Aleksiejczyk 13 Some results on magic matrices Marek Aleksiejczyk University of Warmia and Mazury in Olsztyn, Poland Abstract The aim of this work is to investigate certain properties of magic matrices, i.e. square matrices of order n satisfying the following conditions: (m1) the entries of A belong to the set {1, 2, . , n2} (m2) if (i, j) 6= (k, l) then aij 6= akl (m3) the sums of each row, each column, main diagonal and antidiagonal are equal. We focus our attention to their squares, higher powers and numerical ranges of magic matrices and their powers (we present an estimation in general case and an exact formulas in special cases). Some open problems are also proposed. Keywords Magic matrix, Numerical range. References M. Aleksiejczyk (2002) Properties of numerical ranges of matrices, doctoral disser- tation, Institute of Mathematics of the Polish Academy of Sciences, Warsaw (in Polish) S. J. Kirkland, M. Neumann (1995). Group inverses of Mmatrices associated with nonnegative matrices having few eigenvalues. Linear Algebra Appl. 220,
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