For contributions to hyperbolic systems of conservation laws.

For contributions to numerical methods for partial differential equations, signal processing, and learning.

For contributions to the theory of wavelets and computational harmonic analysis.

For contributions to sparse matrix algorithms and software, including the University of Florida Sparse Matrix Collection.

For fundamental contributions to the development of computational models of coastal storm surges and other complex geophysical phenomena.

For contributions to the theory of splines and other problems related to the approximation of functions.

For fundamental contributions to theory, computation, and application of tensor decompositions.

For contributions to discrete geometry and optimization, polynomial algebra, and mathematical software.

For contributions to concepts and algorithms in numerical multilinear algebra and applications in engineering.

For his fundamental contributions to the mathematical foundations of information and computational sciences.

For contributions to computational geometry and optimization.

For contributions to numerical linear algebra, including the LAPACK project.

For contributions to the theory and applications of nonlinear optimization.

For contributions in modeling, simulation, numerical methods and their diverse applications.

For contributions to numerical linear algebra, data analysis, and machine learning.

For contributions to algebraic geometry and its applications within geometric modeling and in the study of biochemical reaction networks.

For advances in oceanography and climate dynamics.

For contributions to understanding of phenomena in nonlinear and stochastic dynamical systems, turbulent transport, and mixing.

For contributions to numerical linear algebra, including EISPACK, LINPACK, and LAPACK, and high-performance computing.

For contributions to theoretical and computational statistics, signal processing and harmonic analysis.

For contributions in numerical linear algebra and the solution of polynomial and rational eigenvalue problems via linearizations.

For research on numerical methods for partial differential equations and their application to the simulation of flows in porous media.

For contributions to inverse problems, scientific computing, and numerical analysis and their application to hydrocarbon exploration.

For contributions to applied and computational mathematics with applications in material science, computational geometry, and biology.

For contributions to sparse matrix computations.

For contributions to stochastic optimal and adaptive control, filtering theory, and stochastic analysis.

For contributions to stochastics and control.

For contributions to wetting and flow in porous media.

*Deceased