Cauchy Bound

analysis math

Table of Contents

The Cauchy bound limits possible roots of a polynomial to an interval.

Let cauchy_bound_1112425da623ff6e0e1b546b61b2697ab561f223.svg be not the zero-polynomial and cauchy_bound_42bb60940eba490da20f5fa1e64e69d19e226aa0.svg .

For every cauchy_bound_151e4bad86053c426656214bcdb584b1e73a6644.svg with cauchy_bound_310b1cdf5adb2e0167b31bbda230a8e769b8a568.svg we have

cauchy_bound_2f86ad1915fcc976173c942b08c8559c9449f5d4.svg

All roots of cauchy_bound_fa9595cbb51e6e7cca76d13efc6bf6af8d127329.svg lie within the interval cauchy_bound_f430b80e387f8ef7a4a563c595d1e46307b8b862.svg .

Proof

Divide all cauchy_bound_e211ef7faf7cae1ab14facd44a31646a35b7f1c2.svg by cauchy_bound_ef92a14fc8532caace20e6e38aa90be7a7f31fb3.svg , then prove for cauchy_bound_deb4aab517e6a7bcaa308d6cd9fa1d32c1bd9620.svg .

Let cauchy_bound_18608d88489defa349acbb51779f22d4701e2aff.svg and cauchy_bound_f9fcbdd027132a7bc0782e0783ee6bd8ba88072f.svg .

Properties of cauchy_bound_9ffafd4beda5a75e479e24ed287c516ceb19b06f.svg

  • cauchy_bound_25fdf066a95dd9481f8331881d071115f2f7dad5.svg
  • cauchy_bound_0fa45ffcfd1f3ee1d1eccb7d60ad9824e6995cf9.svg
  • cauchy_bound_c503fdb6ee4af006d1e7becc2230955cdd8956ec.svg
cauchy_bound_7f13218a97f7f4336ba9f58f66a271bd9cd43916.svg

If you have an idea how this page could be improved or a comment send me a mail.