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Applied Analysis and AlgebraPublications

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PhD thesis

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


  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. 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.     arXiv version
  3. On indecomposable normal matrices in spaces with indefinite scalar product, Linear Algebra Appl., 259 (1997), 155-168.     arXiv version
  4. Not all GKK $\tau$-matrices are stable, Linear Algebra Appl., 291 (1999), 235-244.     arXiv version
  5. Applications of the duality method to generalizations of the Jordan canonical form, Linear Algebra Appl., 310 (2000), 11-17.     arXiv version
  6. On convergence of infinite matrix products, Electronic J. Linear Algebra, 7 (2000), 178-181.     arXiv version
  7. Open problems on GKK $\tau$-matrices, with Hans Schneider, Linear Algebra Appl., 345 (2002), 263-267.     arXiv version
  8. Hermite-Biehler, Routh-Hurwitz, and total positivity, Linear Algebra Appl., 372 (2003), 105-110.     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.     arXiv version
  10. Real and complex operator norms, with Michael Karow, manuscript, Jul 2004.     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.     arXiv version
  12. M-matrices satisfy Newton's inequalities, Proc. Amer. Math. Soc., 133 (2005), no. 3, 711-717.     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, 395-405.     arXiv version
  14. The inverse eigenvalue problem for symmetric anti-bidiagonal matrices, Linear Algebra Appl., 408 (2005), 268-274.     arXiv version
  15. 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
  16. Fast matrix multiplication is stable, with James Demmel, Ioana Dumitriu and Robert Kleinberg, Numer. Math., 106 (2007), no. 2, 199-224.     arXiv version
  17. Hyperdeterminantal relations among symmetric principal minors, with Bernd Sturmfels, J. Algebra, 316 (2007), no.2, 634-648.     arXiv version
  18. Fast linear algebra is stable, with James Demmel and Ioana Dumitriu, Numer. Math., 108 (2007), 59-91.     arXiv version.
  19. Zonotopal algebra, with Amos Ron, Aug 2007.    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. New coins from old, smoothly, with Fedor Nazarov and Yuval Peres, Aug 2008.    arXiv version.
  23. Compressive sensing: a paradigm shift in signal processing, Dec 2008.    arXiv version.
  24. Communication-optimal parallel and sequential Cholesky decomposition, with Grey Ballard, James Demmel and Oded Schwartz, Feb 2009.    arXiv version.
  25. Minimizing communication in linear algebra, with Grey Ballard, James Demmel and Oded Schwartz, May 2009.    arXiv version.
  26. Computational complexity and numerical stability of linear problems, with Noam Shomron, Jun 2009.    arXiv version.
  27. Hierarchical zonotopal spaces, with Amos Ron and Zhiqiang Xu, Oct 2009.    arXiv version.
  28. Structured matrices, continued fractions, and root localization of polynomials, with Mikhail Tyaglov, Dec 2009.    arXiv version.

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