The J. H. Wilkinson Prize for Numerical Software is awarded every four years to honor outstanding contributions in the field of numerical software. The award is named to commemorate the outstanding contributions of James H. Wilkinson in the same field. The prize was established by Argonne National Laboratory (ANL), the National Physical Laboratory (NPL), and the Numerical Algorithms Group (NAG). They sponsored the award every four years at the International Congress on Industrial and Applied Mathematics (ICIAM) beginning with the 1991 award. By agreement in 2015 among ANL, NPL, NAG, and SIAM, the prize will be administered by the Society for Industrial and Applied Mathematics (SIAM) starting with the 2019 award. Eligibility and selection criteria Candidates must have worked in the field for at most 12 years after receiving their PhD as of January 1 of the award year. Breaks in continuity are allowed, and the prize committee may make exceptions. The award is given on the basis of: Clarity of the software implementation and documentation. Clarity of the paper accompanying the entry. Portability, reliability, efficiency and usability of the software implementation. Depth of analysis of the algorithm and the software. Importance of application addressed by the software. Quality of the test software Winners 1991 The first prize in 1991 was awarded to Linda Petzold for DASSL, a differential algebraic equation solver. This code is available in the public domain. 1995 The 1995 prize was awarded to Chris Bischof and Alan Carle for ADIFOR 2.0, an automatic differentiation tool for Fortran 77 programs. The code is available for educational and non-profit research. 1999 The 1999 prize was awarded to Matteo Frigo and Steven G. Johnson for FFTW, a C library for computing the discrete Fourier transform. 2003 The 2003 prize was awarded to Jonathan Shewchuk for Triangle, a two-dimensional mesh generator and Delaunay Triangulator. It is freely available. 2007 The 2007 prize was awarded to Wolfgang Bangerth, Guido Kanschat, and Ralf Hartmann for deal.II, a software library for computational solution of partial differential equations using adaptive finite elements. It is freely available. 2011 Andreas Waechter (IBM T. J. Watson Research Center) and Carl Laird (Texas A&M University) were awarded the 2011 prize for IPOPT, an object-oriented library for solving large-scale continuous optimization problems. It is freely available. 2015 The 2015 prize was awarded to Patrick Farrell (University of Oxford), Simon Funke (Simula Research Laboratory), David Ham (Imperial College London), and