Scientific Computing FAQ: What is Numerical Analysis?

What is Numerical Analysis?

NA is the union of theoretical and computational investigation into the computer solution of mathematical problems. NA generally includes those problems involving continuous functions of real or complex variables, as opposed to solely discrete variables and functions.

The mixing of theoretical and computational concerns leads to a strong emphasis on algorithms: what are the time and memory usage properties of a certain algorithm? What errors are introduced by an algorithm?

The computational aspects of NA usually take place within the scope of floating-point arithmetic, and are implemented on machines ranging from super-computers through PCs to hand-calculators. The theoretical aspects extend into fields such as Calculus, Differential Equations, and Analysis. The field of Linear Algebra is so often used to model physical systems that the theoretical study of Linear Algebra is in itself often considered to be NA at work.

Primary areas of theoretical concern in NA are:

Global/local error bounding

Stability of algorithms

Rates of convergence of algorithms

Primary areas of computational concern in NA are:

Roundoff error

Global/local error and its tolerance

Time and memory requirements of computation

High Performance Computing (HPC)

Parallel computing

Architecture/platform specific details.