Efficient Evaluation of Polynomials and Exponentials of Polynomials for Equi-Spaced Arguments.
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB
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The evaluation of polynomials at equi-spaced arguments is a recurring task that arises in many applications. When a k-th order polynomial is written in nested form, its evaluation generally requires k additions and k multiplications at each argument of interest. For a set of equi-spaced arguments, it is demonstrated that the multiplications can be entirely circumvented except during initialization and that a recursive procedure employing only k additions per stage will suffice to generate the sequence of polynomial values. For an exponential of polynomial, an even greater savings is possible namely, the exponential can be circumvented except during initialization, and only k multiplications per stage are required in a recursive procedure. Memory storage is also kept at a minimum.
- Theoretical Mathematics