A Convergent Algorithm for Solving Polynomial Algorithms

ABSTRACT

The method of steepest descent is applied in a convergent procedure to determine the zeros of polynomials having either real or complex coefficients. By expressing the polynomials in terms of the Siljak functions, the methods are readily programmed on a digital computer. The significance of the procedures is that their application is straightforward, and not only is convergence rapid in the region of a zero but convergence is guaranteed independent of the initial values.

REFERENCES

• 1: KOKOTOVU, P., AND SmJAK, D. Automatic analog solution of algebraic equations and plotting of root loci by generalized Mitrovic method. IEEE Trans. Appl. and Ind. 83 (1964), 324-328.
• 2: LEVINE, L., AND MEIsszNGER, H. F. An automatic analog computer method for solving polynomials and finding root loci. National Convention Record IRE, Pt. 4 (March 1957), 45- 62.
• 3: G. N. Lance, Solution of Algebraic and Transcendental Equations on an Automatic Digital Computer, Journal of the ACM (JACM), v.6 n.1, p.97-101, Jan. 1959 [doi>10.1145/320954.320961]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Polynomials, methods for

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

General Terms:
Performance, Theory