A Method for the Solution of Roots of a Nonlinear Equation and for Solution of the General Eigenvalue Problem

ABSTRACT

A simple and yet powerful method of solving two of the more common numerical problems is heuristically derived and briefly discussed. The method makes possible the efficient solution of the zeros of a complex function, either transcendental or algebraic, of a complex variable. In addition, it is applicable to the computation of eigen values of a general matrix in which the parameter may appear in any elements of the matrix in a basically unrestricted way. The method is related to the classical secant and regula falsi methods for the finding of real zeros of a real function. Numerical examples of the method applied to several pathological matrices are presented.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Systems of equations

General Terms:
Measurement, Performance, Theory