Standard Polynomials

Overview

NTPoly provides support for computing arbitrary standard polynomials of a matrix.

First, construct a polynomial using the type Polynomial_t. Next, one can set the coefficients of that polynomial using the SetCoefficient routine. Finally the polynomial can be evaluated using either the method of Horner or Paterson and Stockmeyer.

Method

Citation

Here is a reference to the method of Paterson and Stockmeyer.

@article{paterson1973number,
title={On the number of nonscalar multiplications necessary to evaluate polynomials},
author={Paterson, Michael S and Stockmeyer, Larry J},
journal={SIAM Journal on Computing},
volume={2},
number={1},
pages={60--66},
year={1973},
publisher={SIAM}
}

Citing Horner's method is probably optional at this point, but it might make for an enjoyable read:

@article{horner1819xxi,
title={XXI. A new method of solving numerical equations of all orders, by continuous approximation},
author={Horner, William George and others},
journal={Philosophical Transactions of the Royal Society of London},
volume={109},
pages={308--335},
year={1819},
publisher={The Royal Society}
}