Polynomials Root-Finding Using a SLEFE-Based Clipping Method

For finding the real roots of a polynomial,we propose a clipping algorithmcalled SLEFEclipping and an isolation algorithmcalled SLEFEisolation algorithm.Ateach iterative step,the SLEFEclipping algorithm generates two broken lines boundingthe given polynomial.Then,a sequence of intervals can be obtained by computing theintersection of the sequence of broken lines with the abscissa axis.The sequence ofthese intervals converges to the root with a convergence rate of 2.Numerical examplesshow that SLEFE clipping requires fewer iterations and less computation time thancurrent algorithms,and the SLEFE isolation algorithm can compute all intervals thatcontain the roots rapidly and accurately.