Numerical linear algebra is the study of
algorithms for performing
linear algebra computations, most notably
matrix operations, on
computers. It is often a fundamental part of
engineering and
computational science problems, such as
image and
signal processing,
telecommunication,
computational finance,
materials science simulations,
structural biology,
data mining,
bioinformatics,
fluid dynamics, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in
finite difference and
finite element methods.