There are many instances in which the financial world utilizes scientific computing.  In many cases, numbers need to be crunched.  However, there are times when calculations would be very tough that computers cannot perform them in a reasonable amount of time.  As we have learned, there are many ways to simplify the calculations (through nested multiplications, or the Horner’s method for the deflation of a polynomial in factorization, for example).  

In the financial world, datasets are commonly represented as matrices.  Naturally, huge computations would be done on these matrices.  These computations, however, can easily be computed inefficiently.  Just as there are clever tricks in computing polynomials efficiently, there are also methods to compute a matrix efficiently. A very common method of exploring, analyzing, and computing data in matrices is through matrix decompositions.  Matrix decomposition techniques include algorithms such as Q-R factorizations or SVD (singular value decomposition), which are used to reduce the datasets in order to implement efficient matrix algorithms.

Many matrix factorization algorithms have been used in financial analytic systems and simulations.  One application of matrix decomposition methods in finance is the creation of stress tests for market risk in financial instruments.  In large scale financial modelling and analysis, code involving matrices must be efficiently designed to withstand rigorous numeric intensive situations, and to be stable and precise during computation time.  Matrix decomposition is not only used in finance, but in many other fields.

Sources:

http://www.scientific-computing.com/features/feature.php?feature_id=48

http://en.wikipedia.org/wiki/Matrix_decomposition

http://www.geocities.com/mathematicalfinancialeconomics/Documents/Tutorial/MatrixAlgebra.html