Fredrik Johansson
Contact: fredrik.johansson@gmail.com
Postdoc, LFANT, INRIA / IMB, Bordeaux.
Research
My main research topic is arbitrary-precision arithmetic and computation of special functions (hypergeometric functions, the gamma function, the Riemann zeta function, and so forth). I work on developing algorithms that are efficient (both asymptotically and in practice) and also reliable, ideally with provably correct error bounds. More broadly, I'm interested in polynomial arithmetic, numerical analysis, computer algebra, computational number theory, and implementation aspects of mathematical software. I'm the main author of Arb and mpmath, and coauthor of FLINT.
My record computation of the partition function is a fun, if not very practically useful, achievement. While my own work is largely theoretical, high-precision numerical computation is becoming increasingly important in science and engineering, and software that I developed has found use by others in diverse applications such as stellar astrophysics, quantum field theory, antenna design, image processing, computational biology, and free-space optical communication.
Since September 2014, I'm a postdoc at INRIA Bordeaux-Sud-Ouest and Institut de MathÃ©matiques de Bordeaux, working in the LFANT project-team headed by Andreas Enge and Karim Belabas. From 2010 to 2014, I did my PhD in symbolic computation at RISC, Linz, where Manuel Kauers was my advisor. I have an MSc in engineering physics from Chalmers University of Technology, Gothenburg. I was born in Sweden.
Updates
Publications
This list is also available in BibTeX format (txt file).
- F. Johansson. Efficient implementation of elementary functions in the medium-precision range. Submitted. [PDF] [arXiv]
- R. P. Brent, F. Johansson. A bound for the error term in the Brent-McMillan algorithm. To appear in Mathematics of Computation. [PDF] [arXiv]
- F. Johansson. A fast algorithm for reversion of power series. Mathematics of Computation, vol 84, 2015, 475-484. [PDF] [arXiv] [DOI] [info]
- F. Johansson. Fast and rigorous computation of special functions to high precision. PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
- F. Johansson. Evaluating parametric holonomic sequences using rectangular splitting. ISSAC 2014, 256-263. [PDF] [slides] [arXiv] [DOI] [info]
- F. Johansson, B. Nakamura. Using functional equations to enumerate 1324-avoiding permutations. Advances in Applied Mathematics, vol 56, 2014, 20-34. [PDF] [arXiv] [DOI] [info]
- F. Johansson. Rigorous high-precision computation of the Hurwitz zeta function and its derivatives. Numerical Algorithms, 2014. [PDF] [arXiv] [DOI] [info]
- M. Kauers, M. Jaroschek, F. Johansson. Ore polynomials in Sage. To appear in Computer Algebra and Polynomials, Springer Lecture Notes in Computer Science. [PDF] [arXiv] [info]
- F. Johansson. Arb: a C library for ball arithmetic. ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, 166-169. [PDF] [slides] [DOI] [info]
- F. Johansson, M. Kauers, M. Mezzarobba. Finding hyperexponential solutions of linear ODEs by numerical evaluation. ISSAC 2013, 211-218. [PDF] [arXiv] [DOI] [info]
- F. Johansson. Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS Journal of Computation and Mathematics, vol 15, 2012, 341-359. [PDF] [arXiv] [DOI] [info]
Mathematical software
- mpmath - Python library for arbitrary-precision floating-point arithmetic (main author, since 2007)
- Arb - C library for arbitrary-precision ball arithmetic (main author, since 2012)
- FLINT - C library for number theory (coauthor, since 2010)
- ore_algebra - Sage package for holonomic functions (coauthor, 2013)
- Sage (miscellaneous contributions since 2009)
- SymPy (miscellaneous contributions 2007-2008, designed the logo)
I've taken part in Google Summer of Code once as a student and twice as a mentor:
- 2014: mentored Alex Best who implemented Hermite and Smith normal form computation in FLINT
- 2012: mentored Lina Kulakova who implemented algorithms for polynomial factorization in FLINT
- 2008: implemented numerical evaluation in SymPy, mentored by Ondrej Certik
In summer 2009 and 2010, I worked on Sage and mpmath as a contractor for the American Institute of Mathematics, thanks to funding provided by William Stein.
Talks
- September 2014: Reliable multiprecision arithmetic for number theory, LFANT seminar, IMB, Bordeaux
- July 2014: Evaluating parametric holonomic sequences using rectangular splitting, ISSAC 2014, Kobe University, Japan
- May 2014: Making change for 10^{20}, seminar, TU Kaiserslautern
- March 2014: Making change for 10^{20}, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- October 2013: Progress on algorithms for high-precision evaluation of special functions, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- July 2013: Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2013 SIAM Annual Meeting, San Diego, CA
- June 2013: Arb: a C library for ball arithmetic, ISSAC 2013, Boston, MA [Received the ISSAC 2013 Distinguished Software Presentation Award]
- June 2013: Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation, ISSAC 2013, Boston, MA
- March 2013: Fast, rigorous, arbitrary precision numerics with ball arithmetic, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- November 2012: Algorithms for hyperexponential solutions of differential equations, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- May 2012: Fast special function computations with FLINT, RISC-DESY Workshop, RISC, Hagenberg.
- December 2011: Fast combinatorial special functions, Sage Days 35: Algorithms in Number Theory and FLINT, University of Warwick
- November 2011: Partitions in the quintillions or Billions of congruences, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- November 2011: Fast reversion of power series, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- July 2010: Computation of special functions in mpmath, Sage Days 24: Symbolic Computation in Differential Algebra and Special Functions, RISC, Hagenberg
- July 2010: Computation of special functions in mpmath, Sage Days 23: Number Theory and Algebra, Lorentz Center, Leiden
- May 2009: mpmath: arbitrary-precision floating-point arithmetic and special functions, Sage Days 15, University of Washington, Seattle, WA
Music
- I compose MIDI music.
- What I'm listening to: my last.fm account.
Doom
My Doom maps and related information.