Publications



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    Articles

  1. Classification of normal operators in spaces with indefinite scalar product of rank 2, with V. A. Strauss, Linear Algebra Appl., 241-3 (1996) , 455-517.     cmpclass.ps     cmpclass.pdf     arXiv version

  2. On classification of normal operators in real spaces with indefinite scalar product, with V. A. Strauss, Linear Algebra Appl., 255 (1997), 113-155.     rlclass.ps     rlclass.pdf     arXiv version

  3. On indecomposable normal matrices in spaces with indefinite scalar product, Linear Algebra Appl., 259 (1997), 155-168.     indecomp.ps     indecomp.pdf     arXiv version

  4. Not all GKK $\tau$-matrices are stable, Linear Algebra Appl., 291 (1999), 235-244.     gkktau.ps     gkktau.pdf     arXiv version

  5. Applications of the duality method to generalizations of the Jordan canonical form, Linear Algebra Appl., 310 (2000), 11-17.     duality.ps     duality.pdf     arXiv version

    Corrected the proof of Theorem 1 (paragraph 2) on 05 Feb 01, thanks to Carl de Boor.

  6. On convergence of infinite matrix products, Electronic J. Linear Algebra, 7 (2000), 178-181.     infprod.ps     infprod.pdf     arXiv version

  7. Open problems on GKK $\tau$-matrices, with Hans Schneider, Linear Algebra Appl., 345 (2002), 263-267.     challenge.ps     challenge.pdf     arXiv version

  8. Hermite-Biehler, Routh-Hurwitz, and total positivity, Linear Algebra Appl., 372 (2003), 105-110.     hbrhtp.ps     hbrhtp.pdf     arXiv version

  9. Potter, Wielandt, and Drazin on the matrix equation $AB=\omega BA$: new answers to old questions, with Volker Mehrmann and Hans Schneider, Amer. Math. Monthly, 111:8 (2004), 655-667.     hms.ps    hms.pdf     arXiv version

  10. Real and complex operator norms, with Michael Karow, manuscript, Jul 2004.     norms.ps    norms.pdf     arXiv version

  11. Approximation orders of shift-invariant subspaces of $W_2^s(R^d)$, with Amos Ron, J. Approx. Theory, 132/1 (2005), 97-148.     apporders.ps    apporders.pdf     arXiv version

  12. M-matrices satisfy Newton's inequalities, Proc. Amer. Math. Soc., 133 (2005), no. 3, 711-717.     newton.ps    newton.pdf     arXiv version

  13. Evaluation of Sylvester type determinants using block-triangularization, in Advances in Analysis, Proceedings of the 4th International ISAAC Congress (H.G.W. Begehr et al, eds.), World Scientific, 2005, pp. 395-405.     sylvester.ps    sylvester.pdf     arXiv version

  14. The inverse eigenvalue problem for symmetric anti-bidiagonal matrices, Linear Algebra Appl., 408 (2005), 268-274.     iep.ps     iep.pdf     arXiv version

  15. Toward accurate polynomial evaluation in rounded arithmetic (short report), with James Demmel and Ioana Dumitriu, Proceedings of the Dagstuhl Seminar "Algebraic and numerical algorithms and computer-assisted proofs" (B. Buchberger et al, eds.), 2005.     dagstuhl.ps    dagstuhl.pdf     Dagstuhl version

  16. Toward accurate polynomial evaluation in rounded arithmetic, with James Demmel and Ioana Dumitriu, Foundations of Computational Mathematics: Santander 2005 (L. Pardo et al, eds.) Cambridge University Press, 2006, pp. 36-105.     eval.ps    eval.pdf     arXiv version

  17. Fast matrix multiplication is stable, with James Demmel, Ioana Dumitriu and Robert Kleinberg, Numer. Math., 106 (2007), no.2, 199-224.     matmul.ps    matmul.pdf     arXiv version

  18. Hyperdeterminantal relations among symmetric principal minors, with Bernd Sturmfels, J. Algebra, 316 (2007), no.2, 634-648.     hyperdet.ps    hyperdet.pdf     arXiv version

  19. Fast linear algebra is stable, with James Demmel and Ioana Dumitriu, Numer. Math., 108 (2007), no.1, 59-91.     linalg.ps     linalg.pdf     arXiv version.

  20. Functions preserving nonnegativity of matrices, with Gautam Bharali, SIAM J. Matrix Anal. Appl., 30 (2008), no.1, 84-101.     olgautam.ps    olgautam.pdf     arXiv version

  21. Accurate and efficient expression evaluation and linear algebra, with James Demmel, Ioana Dumitriu and Plamen Koev, Acta Numerica, 17 (2008), 87-145.     acta_num.ps    acta_num.pdf    arXiv version.

  22. Compressive sensing: a paradigm shift in signal processing, Dec 2008.    csensing.ps    csensing.pdf    arXiv version.

  23. Communication-optimal parallel and sequential Cholesky decomposition, with Grey Ballard, James Demmel and Oded Schwartz, SIAM J. Sci. Comput. 32 (2010), no. 6, 3495-3523.    cholesky.ps    cholesky.pdf    arXiv version.

  24. Computational Complexity and Numerical Stability of Linear Problems, with Noam Shomron, Proceedings of the 5th European Congress of Mathematics, A.C.M. Ran, H. te Riele, J. Wiegerinck (Eds.), EMS Publishing House, 2010, pp. 381-400.    ccnsla.ps    ccnsla.pdf    arXiv version.

  25. Zonotopal algebra, with Amos Ron, Adv. Math. 227 (2011), no.2, 847-894.     zonotopes.ps    zonotopes.pdf    arXiv version.

  26. New coins from old, smoothly, with Fedor Nazarov and Yuval Peres, Constr. Approx. 33 (2011), 331-363.    coins.ps    coins.pdf    arXiv version.

  27. Minimizing communication in linear algebra, with Grey Ballard, James Demmel and Oded Schwartz, SIAM J. Matrix Anal. Appl. 32 (2011), no. 3, 866-901.    mincomm.ps    mincomm.pdf    arXiv version.

  28. Graph expansion and communication costs of fast matrix multiplication, with Grey Ballard, James Demmel and Oded Schwartz, SPAA 2011, 1-12.    expansion.ps     expansion.pdf     arXiv version.

  29. Hierarchical zonotopal spaces, with Amos Ron and Zhiqiang Xu, Trans. Amer. Math. Soc. 364 (2012), 745-766.    hierarchy.ps    hierarchy.pdf    arXiv version.

  30. Structured matrices, continued fractions, and root localization of polynomials, with Mikhail Tyaglov, SIAM Review, 54 (2012), no.3, 421-509.    RF.ps    RF.pdf    arXiv version.

  31. Szegő's theorem for matrix orthogonal polynomials, with Maxim Derevyagin, Sergey Khrushchev and Mikhail Tyaglov, J. Approx. Theory, 164/9 (2012), 1238-1261.    szego.ps    szego.pdf    arXiv version.

  32. Communication-optimal parallel algorithm for Strassen's matrix multiplication, with Grey Ballard, James Demmel, Benjamin Lipshitz and Oded Schwartz, SPAA 2012, 193-204.    caps.ps     caps.pdf     arXiv version.

  33. Strong scaling of matrix multiplication algorithms and memory-independent communication lower bounds, with Grey Ballard, James Demmel, Benjamin Lipshitz and Oded Schwartz, SPAA 2012, 77-79.    strongscale.ps     strongscale.pdf     arXiv version.

  34. Matrices that commute with their derivative. Research and historical note, with Volker Mehrmann and Hans Schneider, Jul 2012.     commute.ps     commute.pdf     arXiv version.

  35. Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication, with Grey Ballard, James Demmel, Benjamin Lipshitz and Oded Schwartz, Design and Analysis of Algorithms, Vol. 7659, 2012, pp. 13-36.     rectangle.ps     rectangle.pdf     arXiv version.