It is also convenient to define the zeroth divided difference of to be itself:
Some important properties of divided differences are:
If is a polynomial of order and , then the -th divided differences of vanish identically
If is a polynomial of order , then is a polynomial in of order .
Divided differences are useful for interpolating functions when the values are given for unequally spaced values of the argument.
Becuse of the first property listed above, it does not matter with respect to which two arguments we compute the divided difference when we compute the -st divided difference from the -th divided difference. For instance, when computing the divided difference table for tabulated values of a function, a convenient choice is the following:
|Date of creation||2013-03-22 14:40:59|
|Last modified on||2013-03-22 14:40:59|
|Last modified by||rspuzio (6075)|