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`We have a set of data points for
which, for example, represent time moments and measurements.
We want to find a relationship (function) that gives .
For this, we consider a set of predefined functions
and claim that the relationship
is of the form
`

`
where the parameters are unknown for the moment and will be determined
based on the data.
Usually the number of parameters is much smaller than the number of data pairs,
`

`
For example, if and we use polynomial functions
, , we recover the previous example,
where we fitted a quadratic function; in this example .
`
`To determine we insert the data in the relation ()
and obtain the following equation
`

`
Denoting
`

`
the equations become
`

`
This system has rows (equations) and only columns (unknowns), with .
Therefore we can only find a solution in an approximative sense.
`

** Next:** The Calculus Approach
** Up:** Linear Least Squares
** Previous:** Least Squares Data Fitting
** Contents**
Adrian Sandu
2001-08-26