Mathematical problems arise across a plethora of scientific and engineering areas. Numerical analysis is a broad area that focuses on the development and theoretical analysis of algorithms for provably solving such problems, with an eye towards computational efficiency and stability.  This often incorporates mathematical and computational tools from linear algebra, analysis, modeling, and scientific computing, to name a few. Depending on the specific method and application area, numerical analysis also interacts with many branches of mathematics including analysis, geometry and topology, algebra, and probability and statistics.

Members of the numerical analysis group at UCSD have broad research interests and expertise, reflecting the breadth of numerical analysis. Their interests range from random graphs and random matrix theory, to geometric mechanics and differential geometry, harmonic analysis and signal processing, PDEs and multi-scale modeling, and machine learning and data science.


Photo of Alex Cloninger
Alex Cloninger

Research Areas

Geometric Data Analysis

Machine Learning

Applied Harmonic Analysis

Photo of Ioana Dumitriu
Ioana Dumitriu

Research Areas

Discrete Probability

Stochastic Eigenanalysis

Scientific Computing

Numerical Linear Algebra

Applications in Machine Learning

Photo of Melvin Leok
Melvin Leok

Research Areas

Numerical Analysis

Computational Geometric Control Theory

Computational Geometric Mechanics

Photo of Rayan Saab
Rayan Saab

Research Areas

Mathematics of Data

Information Theory

Applied and Computational Harmonic Analysis

Signal Processing

Photo of Xiaochuan Tian
Xiaochuan Tian

Research Areas

Peridynamics and Nonlocal Models

Additional Faculty

Photo of Philip Gill
Philip Gill

Research Areas

Numerical Analysis

Software for Optimization

Scientific Computation

Numerical Linear Algebra

Numerical Optimization

Photo of Michael Holst
Michael Holst

Research Areas

Numerical Analysis

Partial Differential Equations

Mathematical Physics

Applied Analysis