This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 Further Examples: Interpolation Approximating Sqrt Here is a table of values of the square root function at the points . In[1]:= Out[1]= This constructs an approximate function that represents these 10 values on the domain . In[2]:= Out[2]= The values of the function match the data at the given points. In[3]:= Out[3]= The function sqrt1 also gives a fair approximation to the square root function at other points between and . In[4]:= Out[4]= A plot of the difference between the two functions shows that the approximation is better at some points than at others. In[5]:= Here is another set of data that gives values of the square root function as well as its derivatives at the points . In[6]:= Out[6]= Here is the corresponding interpolating function. In[7]:= Out[7]= The values of this function likewise match the data at the given points. In[8]:= Out[8]= Here is the plot of the difference between the square root function and sqrt2. In[9]:= This shows that in general sqrt2 gives a significantly better approximation to the square root function than sqrt1 does. In[10]:= Out[10]= In[11]:= Finding Closest Integers This defines the function closestIntegers which returns the integers in list1 that are closest to those in list2. In[12]:= In[13]:= Out[13]= Periodic Interpolation This creates an InterpolatingFunction object which repeats itself periodically. The data at the endpoints of the fundamental period must match: otherwise the function would not be periodic. In[14]:= In[15]:= In more than one dimension, you can specify that some dimensions be repeated periodically and that others are not by giving the value of the option as a list. This sets up an InterpolatingFunction which will be periodic in the second dimension but not in the first. In[16]:= In[17]:= In[18]:= In[19]:=