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.

### Faculty

##### Ioana Dumitriu

Research Areas

Discrete Probability

Stochastic Eigenanalysis

Scientific Computing

Numerical Linear Algebra

Applications in Machine Learning

##### Melvin Leok

Research Areas

Numerical Analysis

Computational Geometric Control Theory

Computational Geometric Mechanics

##### Rayan Saab

Research Areas

Mathematics of Data

Information Theory

Applied and Computational Harmonic Analysis

Signal Processing

### Additional Faculty

##### Philip Gill

Research Areas

Numerical Analysis

Software for Optimization

Scientific Computation

Numerical Linear Algebra

Numerical Optimization

##### Michael Holst

Research Areas

Numerical Analysis

Partial Differential Equations

Mathematical Physics

Applied Analysis