IGNOU BCA Solved Assignment 5th SEM

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BCA Solved Assignment 5th Sem

1) Explain each of the following with at least one suitable example:
(i) Non-associativity of computer arithmetic
(ii) Loss of significant digits
(iii) Floating point representation of numbers
(iv) Pivoting
(v) Rounding error in computation
(vi) ILL - CONDITIONED EQUATION
(vii) Instability of an algorithm
(viii) Underflow
(ix) Order of convergence of an iterative method
(x) Order of a numerical method.
Non-associativity of computer arithmetic
A binary operation on a set S that does not satisfy the associative law is called non-associative.
Symbolically,
For such an operation the order of evaluation does matter. For example:
Subtraction
Also note that infinite sums are not generally associative, for example:
Whereas
The study of non-associative structures arises from reasons somewhat different from the mainstream of
classical algebra. One area within non-associative algebra that has grown very large is that of Lie
algebras. There the associative law is replaced by the Jacobi identity. Lie algebras abstract the essential
nature of infinitesimal transformations, and have become ubiquitous in mathematics. They are an
example of non-associative algebras.
There are other specific types of non-associative structures that have been studied in depth. They tend
to come from some specific applications. Some of these arise in combinatorial mathematics. Other
examples: Quasigroup,Quasifield, No associative ring.

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