Books and Book Chapters
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Riemann--Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions, (T. Trogdon and S. Olver), SIAM, 2016 Sample .pdf
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A Unified Numerical Approach for the Nonlinear Schrodinger Equations, (T. Trogdon). Unified transform method for boundary value problems: applications and advances , (B. Pelloni and A. S. Fokas (Eds.)), SIAM, 2015.
Dissertation
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Riemann--Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions .pdf (.pdf with front matter)
Numerical Analysis and Approximation Theory
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Benchmarking numerical methods for lattice equations using the Toda lattice, submitted, (D. Bilman and T. Trogdon). .pdf
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Smoothed analysis for the conjugate gradient algorithm , SIGMA, 2016, Vol. 12, (G. Menon and T. Trogdon). .pdf
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Fast computation of Gauss quadrature nodes and weights on the whole real
line , IMA J. Numer. Anal., 2016, Vol. 36, (A. Townsend, T. Trogdon and S. Olver). .pdf
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Rational approximation, oscillatory Cauchy integrals and Fourier transforms, Constr. Approx., 2016, Vol. 43, (T. Trogdon). .pdf
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A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature , IMA J. Numer. Anal., Vol. 36, (T. Trogdon and S. Olver). .pdf
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On the application of GMRES to oscillatory singular integral equations , BIT Numer. Math., 2015, Vol. 55, (T. Trogdon). .pdf
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Nonlinear steepest descent and the numerical solution of Riemann-Hilbert problems, Comm. Pure Appl. Math., 2014, Vol. 67, (S. Olver and T.
Trogdon). .pdf
Probability and Random Matrix Theory
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The conjugate gradient algorithm on well-condition Wishart matrices is almost deterministic, submitted, (P. Deift and T. Trogdon). arXiv
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On spectral and numerical properties of random butterfly matrices, submitted, (T. Trogdon). .pdf
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Universality in numerical computation with random data. Case studies, analytic results and some spectulations, submitted, (P. Deift and T. Trogdon). .pdf
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Random matrices and the New York City subway system, Phys. Rev. E, Vol. 96, (A. Jagannath and T. Trogdon). .pdf
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Universality for eigenvalue algorithms on sample covariance matrices, SIAM J. Numer. Anal., to appear, (P. Deift and T. Trogdon). .pdf
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Universality for the Toda algorithm to compute the eigenvalues of a random matrix, CPAM, to appear, (P. Deift and T. Trogdon). .pdf
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Universality in halting time and its applications in optimization, Q. Appl. Math., to appear, (L. Sagun, T. Trogdon and Y. LeCun). .pdf
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On the condition number of the critically-scaled Laguerre Unitary Ensemble, DCDS-A, 2016, (P. Deift, G. Menon and T. Trogdon). .pdf
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An extension of the Derrida-Lebowitz-Speer-Spohn equation, Phys. Lett. A, 2015, (C. Bordenave, P. Germain and T. Trogdon). .pdf
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Universality in Numerical Computations with Random Data, PNAS, 2014, Vol. 111, (P. Deift, G. Menon, S. Olver and T. Trogdon). .pdf
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Sampling Unitary Ensembles, Random Matrices Theory Appl., 2015, Vol. 4, (S. Olver, R. R. Nadakuditi and T. Trogdon). .pdf
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Numerical solution of Riemann--Hilbert problems: orthogonal polynomials and random matrix theory, Constr. Approx., 2014, Vol. 39, (S. Olver and T. Trogdon). .pdf
Linear PDEs
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Boundary value problems for evolution partial differential equations with discontinuous data, submitted, (G. Biondini and T. Trogdon). .pdf
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Gibbs phenomenon for dispersive PDEs on the line, SIAM J. Appl. Math., Vol. 77, (G. Biondini and T. Trogdon). .pdf
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The Method of Fokas for Solving Linear Partial Differential Equations, SIAM Review, 2014, Vol. 56, (B. Deconinck, T. Trogdon and V. Vasan). .pdf
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The solution of Linear Constant-Coefficient Evolution PDEs With Periodic Boundary Conditions, Applicable Analysis, 2012, Vol. 91, (T. Trogdon and B. Deconinck). .pdf
Integrable Systems and Inverse Scattering
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On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data, submitted for publication, (D. Bilman and T. Trogdon). arXiv
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Numerical inverse scattering for the sine--Gordon equation, submitted for publication, (B. Deconinck, T. Trogdon and X. Yang). arXiv
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Numerical inverse scattering for the Toda lattice, submitted for publication, (D. Bilman and T. Trogdon). .pdf
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Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results, Physics Letters A, 2014, Vol. 378, (T. Trogdon and B. Deconinck). .pdf
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A numerical dressing method for the nonlinear superposition of solutions of the KdV equation, Nonlinearity, 2013, Vol. 27, (T. Trogdon and B. Deconinck). .pdf
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Numerical computation of the finite-genus solutions of the Korteweg--de Vries equation via Riemann--Hilbert problems , Appl. Math. Lett., 2013, Vol. 16, (T. Trogdon and B. Deconinck). .pdf
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A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution, Physica D, 2013, Vol. 251, (T. Trogdon and B. Deconinck). .pdf
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Numerical inverse scattering for the focusing and defocusing nonlinear Schrodinger equations, Proc. Roy. Soc. Lon. A., 2012, (T. Trogdon and S. Olver). .pdf
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Numerical inverse scattering for the Korteweg-de Vries and modified
Korteweg-de Vries equations, Physica D, 2012,(T.
Trogdon, S. Olver and B. Deconinck). .pdf
Optical Physics
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Neck instability of bright solitary waves in hyperbolic Kerr media, Optics Letters, 2013,(S.-P. Gorza, B. Deconinck, T. Trogdon, P. Emplit and M. Haelterman). .pdf
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Experimental demonstration of the oscillatory snake instability of
the bright soliton of the (2+1)D hyperbolic nonlinear Schrodinger
equation, Physical Review Letters, 2011, (S.-P. Gorza, P.
Emplit, T. Trogdon, B. Deconinck and M. Haelterman). .pdf
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Transverse Instability of Bright Solitons in Hyperbolic dispersive Media, in Nonlinear Photonics, OSA Technical Digest, 2010,(S.-P. Gorza, M. Haelterman, P. Emplit, T. Trogdon and B. Deconinck)..pdf