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Stability of zeros of power series equations
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We prove that if |a1| is large and |a0| is small enough, then every approximate zero of power series equation P∞ n=0 anxn = 0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, anzn + an−1zn−1 + · · · + a1z + a0 = 0 for a given integer n > 1.
Abstract
We prove that if |a1| is large and |a0| is small enough, then every approximate zero of power series equation P∞ n=0 anxn = 0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, anzn + an−1zn−1 + · · · + a1z + a0 = 0 for a given integer n > 1.
참고문헌 (16)
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