- Theorems and counterexamples on structured matrices, PhD Thesis, University of Wisconsin, Madison, July 2000. arXiv version 
- 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 
- 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 
- On indecomposable normal matrices in spaces with indefinite scalar product, Linear Algebra Appl., 259 (1997), 155-168. arXiv version 
- Not all GKK $tau$-matrices are stable, Linear Algebra Appl., 291 (1999), 235-244. arXiv version 
- Applications of the duality method to generalizations of the Jordan canonical form, Linear Algebra Appl., 310 (2000), 11-17. arXiv version 
- On convergence of infinite matrix products, Electronic J. Linear Algebra, 7 (2000), 178-181. arXiv version 
- Open problems on GKK $tau$-matrices, with Hans Schneider, Linear Algebra Appl., 345 (2002), 263-267. arXiv version 
- Hermite-Biehler, Routh-Hurwitz, and total positivity, Linear Algebra Appl., 372 (2003), 105-110. arXiv version 
- 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 
- Real and complex operator norms, with Michael Karow, manuscript, Jul 2004. arXiv version 
- 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 
- M-matrices satisfy Newton's inequalities, Proc. Amer. Math. Soc., 133 (2005), no. 3, 711-717. arXiv version 
- 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 
- The inverse eigenvalue problem for symmetric anti-bidiagonal matrices, Linear Algebra Appl., 408 (2005), 268-274. arXiv version 
- 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 
- Fast matrix multiplication is stable, with James Demmel, Ioana Dumitriu and Robert Kleinberg, Numer. Math., 106 (2007), no. 2, 199-224. arXiv version 
- Hyperdeterminantal relations among symmetric principal minors, with Bernd Sturmfels, J. Algebra, 316 (2007), no.2, 634-648. arXiv version 
- Fast linear algebra is stable, with James Demmel and Ioana Dumitriu, Numer. Math., 108 (2007), 59-91. arXiv version .
- Zonotopal algebra, with Amos Ron, Aug 2007. arXiv version .
- Functions preserving nonnegativity of matrices, with Gautam Bharali, SIMAX, 30 (2008), no.1, 84-101. arXiv version 
- Accurate and efficient expression evaluation and linear algebra, with James Demmel, Ioana Dumitriu and Plamen Koev, Acta Numerica, 17 (2008), 87-145. arXiv version .
- New coins from old, smoothly, with Fedor Nazarov and Yuval Peres, Aug 2008. arXiv version .
- Compressive sensing: a paradigm shift in signal processing, Dec 2008. arXiv version .
- Communication-optimal parallel and sequential Cholesky decomposition, with Grey Ballard, James Demmel and Oded Schwartz, Feb 2009. arXiv version .
- Minimizing communication in linear algebra, with Grey Ballard, James Demmel and Oded Schwartz, May 2009. arXiv version .
- Computational complexity and numerical stability of linear problems, with Noam Shomron, Jun 2009. arXiv version .
- Hierarchical zonotopal spaces, with Amos Ron and Zhiqiang Xu, Oct 2009. arXiv version .
- Structured matrices, continued fractions, and root localization of polynomials, with Mikhail Tyaglov, Dec 2009. arXiv version .
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Translations and editorial work
- V. L. Goncharov, The theory of best approximation of functions , translated from the 1945 Russian original jointly with Vladimir Yegorov. J. Approximation Theory, 106 (2000), no. 1, 2-57.
- U. van Rienen, Numerical Methods in Computational Electrodynamics: Linear Systems in Practical Applications , copy-edited. Springer-Verlag, 2001, 375 pp.
- V. A. Markov, On a question of D. I. Mendeleev , translated from the 1890 Russian original jointly with Carl de Boor. History of Approximation Theory (HAT).
- Special issue of Linear Algebra and its Applications in honor of Friedrich L. Bauer.  (H. Fassbender, M. Griebel, O. Holtz, G. W. Stuart, eds.), 417 (2006), 299-498.
- Yu. S. Barkovsky, Lectures on the Routh-Hurwitz problem, , translated from the Russian original jointly with Mikhail Tyaglov.