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Linear Least Squares Approximation Jami Durkee

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Problem to be Solved Finding Ax=b where there are no solution y=x y=x+2 Interpolation of graphs where there are numerous points or if it is not possible to find – Examples: interpolation of: {(-20,1),(-15,5/2),(-15/2,-2),(0,0),(1,0),(2,3),(4,4),(9,-1),(10,3/2),(11,0)} OR

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Definition Least squares solution- the closest value to x, in this case the closest line to all data points

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How to solve it

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How to develop the algorithm

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example

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Error

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Advantages It can be done using any data points and for as many data points as wanted It is only one variable so it is easier to solve for and graph Several different errors can be found

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Disadvantages It is only an approximation, unless the points are in a line the linear least square will not be on any or all of the points The graph may go through one or more points, but it does not have to so all points could have an error Deciding which error to use

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