Publications

PhD thesis

1. Theorems and counterexamples on structured matrices, PhD Thesis, University of Wisconsin, Madison, July 2000.     arXiv version

Articles

2. 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.     arXiv version

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

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

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

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

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

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

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

10. 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.     arXiv version

11. Real and complex operator norms, with Michael Karow, manuscript, Jul 2004.     arXiv version

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

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

14. 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, 395-405.     arXiv version

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

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 version

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

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

19. Fast linear algebra is stable, with James Demmel and Ioana Dumitriu, Numer. Math., 108 (2007), 59-91.     arXiv version.

20. Functions preserving nonnegativity of matrices, with Gautam Bharali, SIMAX, 30 (2008), no.1, 84-101.     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.    arXiv version.

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

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

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

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

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

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

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

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