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Numerical Analysis Reviewer: Errors, Methods, and Series

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REVIEWER IN NUMERICAL ANALYSIS
Numerical Analysis- deals with the process of
getting the numerical solution to complex problems.
To make a tough Mathematical problem easier to
solve, an approximation is essential.
Random Error - Due to natural fluctuations in
measurement or computational systems. By
definition, these fluctuations are random and
therefore, the average random error is zero
Systematic Error - A repeated “bias” in the
measurement or computational system.
-It is the study of algorithms that use numerical
approximation to well defined mathematical
problems
For engineering applications, an approximation in the
form of a rational number that is “close enough” is
used instead of an irrational number.
Babylonian Method: - Old method for getting the
square root.
-
Once the two values are close, up to an
acceptable level, we say that convergence
has been achieved.
Errors- associated with both calculations and
measurements can be characterized by their
accuracy and precision
Accuracy – Measure of how closely a computed or
measured value agrees with the true value.
Precision - Measure of how closely individual
computed or measured values agree with each other
Degree of Precision
-
For measurement, the smallest value that
can be measured or computed. 15 ±1mm
For computational devices,
- The algorithm of computation- The storage
capacity
- The number of stored digits
Single Precision (6-9 significant digits)
Double Precision (15-17 significant digits)
Arbitrary Precision
Taylor Series- is an expansion of some
function into an infinite sum of terms
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