Modification on Restrictive Taylor and Padé Approximations

We review Taylor approximation (TA), Padé approximation (PA), Restrictive Taylor approximation (RTA) and Restrictive Padé approximation (RPA). After comparing these four approximation methods with two other modified approximation methods: Modified Restrictive Taylor approximation (MRTA) and Modified Restrictive Padé approximation (MRPA), we give test examples to illustrate how the modified approximations could be used. The mathematical principles behind all these approximations could be applied for the development of new computing methods.