The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
It is shown that the problem of evaluating an Nth degree polynomial is reducible to the problem of dividing the polynomial. A method for dividing an Nth degree polynomial by an N/2 degree polynomial in O(N log 2N) steps is given. Using this it is shown that the evaluation of an Nth degree polynomial at N points can be done in O(N log 3N). The related problem of computing of computing the resides of an N precision integer is handed by the same algorithm in O(N log2N loglogN) steps. Using the methods of Horowitz11 and Heindel8 it is shown that interpolation of an Nth degree polynomial is redicible to the problem of evaluating an Nth degree polynomial at N points. An algorithm for preconditioned polynomial interpolation requiring O(N log 2N) steps is presented. This is then extended to perform the complete interpolation in O(N log 3N) steps. A modified version of Reminider Problem in O(N log 2N loglogN) steps.