Dr Behnam Hashemi

School/Department: Computing and Mathematical Sciences, School of

Profile

Before joining the University of Leicester, I worked at Qatar University and Shiraz University of Technology as an associate professor and at the University of Oxford as a postdoc.

Research

My research interests include numerical linear and multilinear algebra, low-rank approximation and self-validated numerical algorithms. During 2014-2017 I worked on the development of Chebfun3, a software package involving 15000 lines of object-oriented MATLAB code for numerical computing with 3D functions defined on a box. I have also worked on matrix theory over ordered semirings. More details about my work can be found at https://sites.google.com/view/bhashemi/research

Publications

Here is a list of most of my journal publications.

B. Hashemi, Y. Nakatsukasa, L.N. Trefethen, Rectangular eigenvalue problems, Advances in Computational Mathematics 48, 80 (2022), full text publicly available at https://doi.org/10.1007/s10444-022-09994-8

B. Hashemi, Y. Nakatsukasa, Least-squares spectral methods for ODE eigenvalue problems, SIAM Journal on Scientific Computing 44 (2022) A3244-A3264, https://doi.org/10.1137/21M1445934

B. Hashemi, Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation, Applied Mathematics Letters 112, 106818 (2021), https://doi.org/10.1016/j.aml.2020.106818

A. Paganini, B. Hashemi, E.A. Ballester, L. Belluzzi, Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation, Astronomy and Astrophysics 645, A4 (2021), full text publicly available at https://doi.org/10.1051/0004-6361/201937149

J.L. Aurentz, B. Hashemi, The Laurent-Horner method for validated evaluation of Chebyshev expansions, Applied Mathematics Letters 102, 106113 (2020), https://doi.org/10.1016/j.aml.2019.106113

A. Frommer, B. Hashemi, Computing enclosures for the matrix exponential, SIAM Journal on Matrix Analysis and Applications 41 (2020) 1674-17037, https://doi.org/10.1137/19M1263431

B. Hashemi, Enclosing Chebyshev expansions in linear time, ACM Transactions on Mathematical Software 45 (2019) 1-33, https://doi.org/10.1145/3319395

B. Hashemi, Y. Nakatsukasa, On the spectral problem for trivariate functions, BIT Numerical Mathematics 58 (2018) 981-1008, full text publicly available at https://doi.org/10.1007/s10543-018-0710-4

B. Hashemi, L.N. Trefethen, Chebfun in three dimensions, SIAM Journal on Scientific Computing 39 (2017) C341-C363, https://doi.org/10.1137/16M1083803

B. Hashemi, H. Tavakolipour, M.N. Shirazi, Explicit formulae for the greatest least-squares and minimum norm g-inverses and the unique group inverse of matrices over commutative residuated dioids, Semigroup Forum 92 (2016) 541-550, full text publicly available at https://doi.org/10.1007/s00233-015-9771-8

B. Hashemi, M.M. Khalilabadi, H. Tavakolipour, A cubic time algorithm for finding the principal solution to Sylvester matrix equations over (max,+), Linear and Multilinear Algebra 63 (2015) 283-295, https://doi.org/10.1080/03081087.2013.860600

B. Hashemi, M.M. Khalilabadi, H. Tavakolipour, On the fixed-point type Sylvester matrix equations over complete commutative dioids, Electronic Journal of Linear Algebra 27 (2014) 882-891, full text publicly available at https://doi.org/10.13001/1081-3810.2864

A. Frommer, B. Hashemi, T. Sablik, Computing enclosures for the inverse square root and the sign function of a matrix, Linear Algebra and its Applications 456 (2014) 199-213, full text publicly available at https://doi.org/10.1016/j.laa.2013.11.047

B. Hashemi, H. Tavakolipour, M.N. Shirazi, Comparison of the quasi-inverses of the Kronecker sum and product of matrices over complete commutative dioids with applications, Linear Algebra and its Applications 448 (2014) 22-36, full text publicly available at https://doi.org/10.1016/j.laa.2014.01.028

A. Frommer, B. Hashemi, Verified stability analysis using the Lyapunov matrix equation, Electronic Transactions on Numerical Analysis 40 (2013) 187-203, full text publicly available at https://etna.ricam.oeaw.ac.at/vol.40.2013/pp187-203.dir/pp187-203.pdf

B. Hashemi, H. Tavakolipour, A non-induced interval matrix norm, Reliable Computing 18 (2013) 144-146, full text publicly available at https://www.cs.utep.edu/interval-comp/reliable-computing-18-pp-144-146.pdf

B. Hashemi, M. Dehghan, The interval Lyapunov matrix equation: Analytical results and an efficient numerical technique for outer estimation of the united solution set, Mathematical and Computer Modelling 55 (2012) 622-633, full text publicly available at https://doi.org/10.1016/j.mcm.2011.08.036

A. Frommer, B. Hashemi, Verified error bounds for solutions of Sylvester matrix equations, Linear Algebra and its Applications 436 (2012) 405-420, full text publicly available at https://doi.org/10.1016/j.laa.2010.12.002

B. Hashemi, M. Dehghan, Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation AX= B, Journal of Computational and Applied Mathematics 235 (2011), 2969-2978, full text publicly available at https://doi.org/10.1016/j.cam.2010.12.015

A. Frommer, B. Hashemi, Verified computation of square roots of a matrix, SIAM Journal on Matrix Analysis and Applications 31 (2010), 1279-1302, https://doi.org/10.1137/090757058

B. Hashemi, M. Dehghan, Efficient computation of enclosures for the exact solvents of a quadratic matrix equation, Electronic Journal of Linear Algebra 20 (2010) 519-536, full text publicly available at https://doi.org/10.13001/1081-3810.1391

M. Dehghan, M. Ghatee, B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, International Journal of Computer Mathematics 86 (2009) 1433-1452, https://doi.org/10.1080/00207160701874789

M. Dehghan, B. Hashemi, Determination of the degrees of P-property and nonnegative invertibility for a fuzzy matrix, International Journal of Approximate Reasoning 46 (2007) 98-108, full text publicly available at https://doi.org/10.1016/j.ijar.2006.09.002

Teaching

I teach MA2042 in Semester 2 of the 2022-2023 academic year.

Activities

I am currently serving on the editorial board of the following journals:

SIAM Journal on Matrix Analysis and Applications (SIMAX), Associate Editor since 2018

Bulletin of the Iranian Mathematical Society (BIMS), Managing Editor since 2022

My earlier professional service includes the following editorial activities:

(Numerical Analysis) Section Editor, Bulletin of the Iranian Mathematical Society (BIMS), Oct. 2019 - Jun. 2022
Member of the editorial board, The Culture and Thought of Mathematics, An expository journal of the Iranian Mathematical Society published in Persian, Oct. 2013 - Sep. 2019

I am also a Reviewer of the Mathematical Reviews of the American Mathematical Society (AMS).