Lloyd N. Trefethen

Lloyd N. Trefethen is affiliated with the University of Oxford in the United Kingdom. Their research spans several fields, predominantly in mathematics, engineering, and computer science, with a focus on areas such as computational mechanics, applied mathematics, and numerical analysis. Their work also covers computational theory and mathematics and mathematical physics, reflecting a broad interdisciplinary approach within computational and theoretical mathematics.

The key topics represented in their work include mathematical functions and polynomials, matrix theory and algorithms, electromagnetic scattering and analysis, advanced numerical methods in computational mathematics, iterative methods for nonlinear equations, numerical methods for differential equations, and advanced numerical analysis techniques.

Trefethen has authored numerous papers published in various prominent venues. Recent papers include:

• "An Algorithm for Real and Complex Rational Minimax Approximation" (2020), SIAM Journal on Scientific Computing
• "Lightning Stokes Solver" (2022), SIAM Journal on Scientific Computing
• "Numerical analytic continuation" (2023), Japan Journal of Industrial and Applied Mathematics
• "Computation of Two-Dimensional Stokes Flows via Lightning and AAA Rational Approximation" (2024), SIAM Journal on Scientific Computing
• "Log-lightning computation of capacity and Green's function" (2021), Maple Transactions

Trefethen has frequently collaborated with several coauthors during their career, including Yuji Nakatsukasa, Daan Huybrechs, Pablo D. Brubeck, Stefano Costa, and Yidan Xue. Collaborative work with these researchers has contributed to the development of numerical and computational methods.

The main publication venues for Trefethen's work include arXiv (Cornell University) with 17 publications, SIAM Journal on Scientific Computing with 5, SIAM Review with 4, BIT Numerical Mathematics with 2, and SIAM Journal on Numerical Analysis with 2 publications.

In addition to research papers, Trefethen has published several books. These include:

• Society for Industrial and Applied Mathematics: "Numerical Linear Algebra, Twenty-fifth Anniversary Edition" (2022) and "An Applied Mathematician's Apology" (2022)
• Princeton University Press: "Spectra and Pseudospectra" (2020)
• American Mathematical Society: "Numerical Conformal Mapping" (expected 2025)

The scientist has received multiple honors during their career: they became a Fellow of the Royal Society in the United Kingdom in 2005, a Member of the National Academy of Engineering in 2007 for contributions to stability theory in numerical analysis and its application to turbulence onset, a SIAM Fellow in 2009 for contributions to numerical analysis and scientific computing, a Fellow of the American Mathematical Society in 2013, a Member of Academia Europaea in 2019, and a Fellow of the American Association for the Advancement of Science in 1992.