The first question is why, if you are managing doubles, you are dealing with Strings. It should be better if you used the doubles and just set the format in the CellRenderer for that column.
Anyway, what you are looking for may be this: http://download.oracle.com/javase/tutorial/uiswing/examples/components/TableSorterDemoProject/src/components/TableSorter.java
EDIT: If somehow the translation from Double to your representation is complicated, I would create a Comparable class that contains both the Double number and the String representation. Equals(), hashcode() and compareTo() would be implemented using the value of the double; the cellRenderer() and toString() would use the String representation.