Notes  Numerical Methods
Numerical methods for simulation and data analysis are widely used in both systems and synthetic
biology. In this part of the course you will investigate three different numerical methods:
1 . Solving Differential Equations
2. Solving nonlinear equations
3. Fitting data to models
Methods for solving stochastic models will be dealt with in a separate assignment.
1. Basic Concepts in Numerical Analysis
All numerical methods involve approximations due to either limits in the algorithm or physical limits in
the computer hardware. Errors associated with measurements or calculations can be characterized with
reference to
accuracy
and
precision
.
Accuracy
refers to how closely a computed or measured value agree with the
true
value.
Precision
refers to how close measured or computed values agree with each other after repeated
sampling.
Nether Precise NOR accurate:
Precise, but NOT accurate:
Accurate but NOT precise:
Precise AND accurate
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View Full DocumentSimple Error Definitions
There are a number of ways to describe errors in measurements and calculations. The simplest is the
absolute error
, this is the difference between the measured or calculated value and the true value.
A shortcoming of the absolute error is that it doesn
’
t take into account the order of magnitude of the
value under consideration. One way to account for the magnitude is to consider instead the
relative
error
.
Many numerical methods are interative, that is they involve repeating the same calculation many times.
In terms of error analysis, two types of error emerge,
local
and
global
errors. The local error is the error
introduced during one operation of the iterative process. The global error is the accumulative error over
many iterations. Note that the global error is not simply the sum of the local errors due to the nonlinear
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 Spring '07
 Gallivan
 Numerical Analysis, double precision, single precision

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