- Accurate and efficient linear algebra and related algorithms:
computational complexity and numerical stability of sequential and parallel
linear algebra algorithms, stability of multivariate polynomial evaluation
in floating point arithmetics.
- Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz, Graph expansion and communication costs of fast matrix multiplication, J. ACM 59 (2012), no. 6, Art. 32, 23 pp.
- Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz, Minimizing communication in numerical linear algebra, SIAM J. Matrix Anal. Appl. 32 (2011), no. 3, 866-901.
- Olga Holtz and Noam Shomron, Computational complexity and numerical stability of linear problems, European Congress of Mathematics, 381-400, Eur. Math. Soc., Zurich, 2010. arXiv version.
- Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz, Communication-optimal parallel and sequential Cholesky decomposition, SIAM J. Sci. Comput. 32 (2010), no. 6, 3495-3523. arXiv version.
- James Demmel, Ioana Dumitriu, Olga Holtz and Plamen Koev, Accurate and efficient expression evaluation and linear algebra, Acta Numerica, 17 (2008), 87-145. arXiv version.
- James Demmel, Ioana Dumitriu and Olga Holtz, Fast linear algebra is stable, Numer. Math., 108 (2007), 59-91. arXiv version.
- James Demmel, Ioana Dumitriu, Olga Holtz and Robert Kleinberg, Fast matrix multiplication is stable, Numer. Math., 106 (2007), no. 2, 199-224. arXiv version
- James Demmel, Ioana Dumitriu and Olga Holtz, Toward accurate polynomial evaluation in rounded arithmetic,
Foundations of Computational Mathematics: Santander 2005
(L. Pardo et al, eds.) Cambridge University Press, 2006, pp. 36-105.
Direct and inverse problems of core linear algebra: The inverse eigenvalue problem
for nonnegative matrices and its variants, eigenvalue localization of special matrix classes,
Markov chains, other related problems and probability and combinatorics.
- Olga Holtz, Volker Mehrmann and Hans Schneider, Matrices that commute with their derivative. On a letter from Schur to Wielandt, arXiv version
- Gautam Bharali and Olga Holtz, Functions preserving nonnegativity of matrices,
SIMAX, 30 (2008), no.1, 84-101.
- Nenad Moraca, Bounds for norms of the matrix inverse and the smallest singular value,
Linear Alg. Appl., 429 (2008), no.10, 2589-2601.
- Olga Holtz and Bernd Sturmfels, Hyperdeterminantal relations among symmetric principal minors,
J. Algebra, 316 (2007), no.2, 634-648. arXiv version
Root localization and asymptotics of polynomials:
matrix criteria for stability and root location, applications to probability and
theoretical computer science, connections with scalar- and matrix-valued orthogonal
polynomials, including their asymptotics.
- Olga Holtz and Mikhail Tyaglov, Structured matrices, continued fractions, and root localization of polynomials, SIAM Rev. 54 (2012), no. 3, 421-509. arXiv version.
- Yury S. Barkovsky, Mikhail Tyaglov, Hurwitz rational functions, Linear Algebra Appl. 435 (2011), no. 8, 1845-1856. arXiv version.
- Vladimir Kostov, Boris Shapiro, Mikhail Tyaglov, Maximal univalent disks of real rational functions and Hermite-Biehler polynomials, Proc. Amer. Math. Soc. 139 (2011), no. 5, 1625-1635. arXiv version.
- Mikhail Tyaglov, On the number of real critical points of logarithmic derivatives and the Hawaii conjecture, J. Anal. Math. 114 (2011), 1-62.
- Mikhail Tyaglov, Generalized Hurwitz polynomials, May 2010. arXiv version.
- Diego Dominici, Fisher information of orthogonal polynomials I,
J. Comput. Appl. Math. 233 (2010), no. 6, 1511-1518.
- Diego Dominici, Polynomial solutions of nonlinear integral equations,
J. Phys. A 42 (2009), no. 20, 205201, 8 pp.
- Diego Dominici, Asymptotic analysis of the Bell polynomials by the ray method,
J. Comput. Appl. Math. 233 (2009), no. 3, 708-718.
- Yury Barkovsky (translated by Olga Holtz and Mikhail Tyaglov), Lectures on the Routh-Hurwitz problem, Feb 2008.
The algebra of box splines and zonotopes: connections between polynomial
spaces, polynomial ideas, constant-coefficient PDEs, multivariate difference
equations, multivariate polynomial interpolation,
tilings and integer points in zonotopes, combinatorics of
hyperplane arrangements, and various counting functions on graphs.
- Matthias Lenz, Matroids and log-concavity, Jun 2011.
- Matthias Lenz, Hierarchical zonotopal power ideals, European J. Combin.
33 (2012), no. 6, 1120-1141.
- Olga Holtz, Amos Ron and Zhiqiang Xu, Hierarchical zonotopal spaces,
Trans. Amer. Math. Soc. 364 (2012), no. 2, 745-766.
- Bernd Sturmfels and Zhiqiang Xu, Sagbi bases of Cox-Nagata rings,
J. Eur. Math. Soc. (JEMS) 12 (2010), no. 2, 429-459.
- Olga Holtz and Amos Ron, Zonotopal algebra, Adv. Math. 227 (2011),
no. 2, 847-894. arXiv version.
Interplay between approximation theory and other fields: connections between
approximation theory, classical geometry and analysis, algorithms, and probability theory.
- Olga Holtz, Fedor Nazarov and Yuval Peres, New coins from old, smoothly,
Constr. Approx. 33 (2011), no. 3, 331-363.
- Shaowei Lin, Bernd Sturmfels and Zhiqiang Xu, Marginal likelihood integrals for mixtures of independence models, J. Mach. Learn. Res. 10 (2009), 1611-1631.