{"title":"Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves","authors":"Taweechai Nuntawisuttiwong, Natasha Dejdumrong","country":null,"institution":"","volume":152,"journal":"International Journal of Computer and Information Engineering","pagesStart":440,"pagesEnd":445,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10010689","abstract":"Newton-Lagrange Interpolations are widely used in
\r\nnumerical analysis. However, it requires a quadratic computational
\r\ntime for their constructions. In computer aided geometric design
\r\n(CAGD), there are some polynomial curves: Wang-Ball, DP and
\r\nDejdumrong curves, which have linear time complexity algorithms.
\r\nThus, the computational time for Newton-Lagrange Interpolations
\r\ncan be reduced by applying the algorithms of Wang-Ball, DP and
\r\nDejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong
\r\nalgorithms, first, it is necessary to convert Newton-Lagrange
\r\npolynomials into Wang-Ball, DP or Dejdumrong polynomials. In
\r\nthis work, the algorithms for converting from both uniform and
\r\nnon-uniform Newton-Lagrange polynomials into Wang-Ball, DP and
\r\nDejdumrong polynomials are investigated. Thus, the computational
\r\ntime for representing Newton-Lagrange polynomials can be reduced
\r\ninto linear complexity. In addition, the other utilizations of using
\r\nCAGD curves to modify the Newton-Lagrange curves can be taken.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 152, 2019"}