Illustrative Example for Multiplicity Computation Using the Cauchy Index

• p(x) = (x-1/2)5 = 0

• A root of p(x), [ ] = [0.49,0.51].

• P(z); (z = x+iy)

• Create

• Calculate the Cauchy index

  • Roots of f(x, 3) = 0
  • Calculation of
  • 
    

• Roots No. 2, 3, and 4 are selected since they lie within the interval [ ].

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