Next: What is the L1 Up: EXAMPLES Previous: Statics

## Curve through two points

Consider values along a horizontal x-axis ranging from 1 to 100. Suppose at x=1, the y value is given to be y1=1. Likewise at x=100 the y value is given to be y100=100. Now we are to find all the intervening points, .Let us use the L1 criterion
 (7)
The solution to this problem is any curve with a positive slope since all such curves result in the same value of 99 for (7) That is quite a lot of curves!

Now we begin to appreciate the strange flavor of L1. We appreciate the idea that solutions are intervals''. But it is distressing to realize that we could often have graphical difficulty displaying the results. In practice we might need to settle for seeing some examples.'' Perhaps a satisfactory way of generating those examples would be by using random starting values for the fitting.

Suppose we set up the Busch problem with L1. Perhaps we will find the solution is not a unique surface. It might turn out to be a mat'' of variable thickness. It would be annoying to try to display the thickness, but perhaps the thickness is related to the uncertainty of the result. That should have value.

Next: What is the L1 Up: EXAMPLES Previous: Statics
Stanford Exploration Project
4/27/2000