## An Algorithm and Computer Program to Locate Real Zeros of Real Polynomials |

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10000E+01 Laguerre method 190 CONTINUE absolute value array of coefficients BOUND closed interval CALL CHECK complex zeros COMPUTER PROGRAM Continued Subroutine determined distinct real zeros DISTINCT ZEROES Flow chart FORTRAN FOURTH-ORDER POLYNOMIAL IDIMP IDIMX dimension IDIMY Imaginary Real Imaginary iteration Jenkins-Traub method Proposed Laguerre method Newton-Raphson Laguerre's LOCATE REAL ZEROS method Jenkins-Traub method method Newton-Raphson method method Proposed method method will converge method Zeros Zeros Newton-Raphson method Jenkins-Traub non-simple zeros number of distinct number of real ordered from smallest polynomial has complex polynomial Subroutine arguments polynomial with complex probability of convergence proposed algorithm Proposed method Zeros rate of convergence Real Imaginary Real real polynomial Real zeros Real RETURN END APPENDIX smallest to largest status of completion Subroutine listing SYNTHETIC DIVISION Theorem vector of coefficients zeros of p(x ZEROS OF REAL ZEROS Polynomial coefficients zeros Real Imaginary Zeros Real zeros zeros which form Zeros Zeros Real Zeros Zeros Zeros