Numerical Analysis is different from Numerical Computations.
Numerical Analysis can be described as the mathematical analysis of numerical problems and the synthesis of methods for solving them. In Numerical Analysis, methods that use mathematical abstraction and methods to model the solution of numerical problems are studied.
These numerical methods supply a rich assortment of solution tools with comment on their relevance, capabilities and limitations in specific situations. The methods are presented in a formal mathematical way devoid of relevance to practical implementation.
Numerical computations goes a step further. First, based on the mathematical methods developed in numerical analysis, it uses numerical or algebraic description of a problem to development of a solution algorithm that can be implemented on a computer system.
Numerical computations also addresses issues relating to the context in which a solution algorithm is expected to perform well and its reliability in terms of accuracy, stability, effectiveness and efficiency. The purpose behind computation is to gain scientific insight into practical situation and/or deployment of a solution to practical problem; not numeration in itself alone.
Numerical Computations is an engineering (using scientific knowledge to solve practical problems) task as it involves:
1. Problem analysis,
2. Solution method selection,
3. Solution algorithm design,
4. Algorithm implementation: program coding,
5. Program evaluation
6. Solution interpretation and optimisation.
Fundamentally, the foundation of Numerical Computations is the solution methods developed in mathematical numerical analysis. The digital computer is the modern computing tool. Numerical computations also addresses issues relating to the context in which a solution algorithm is expected to perform well and its reliability in terms of accuracy, effectiveness and efficiency. Though numerical methods is fundamental to numerical computations, Numerical Analysis (Scheid, 2006) is different from Numerical computations.
Difference Between Numerical Analysis And Numerical Computations
|Ser. No.||Numerical Analysis/Methods||Numerical Computations|
|1||Solution to abstract (ideal situation) problem is in focus.||Solution to practical (real situation)
problem is in focus.
|2||No implementation tool is in view.||A computational instrument for implementation is in view.|
|3||Solution process finiteness is assumed or estimated.||Solution process must be finite or definite, data and process must be bounded.|
|4||The concept of zero and infinity are
used in the formulation of problem
|The concept of zero and infinity considered ambiguous; precise values must be
specified and used in problem formulation and solution.
|5||Error based on mathematical estimates only.||Error based on a combination of machine
precision and mathematical estimates.
|6||Attention is on generalisation of solution method.||Solution specific to problem context and
attention is on the potentials for error reduction.
|7||Proof is sufficient for validity of solution method.||Effectiveness at reproducing the behaviour of the problem being solved is
necessary and consistency of the process
are used for solution validation.
|8||Solution is intended to be communicated to a human agent and must be
|Solution must be communicated to a
computing agent and may differ (e.g. in
precision) may change from machine to
|9||Language use and the primary target of solution communication is a
|Language use and the primary target of
solution communication is a machine