the root of some function <span class="emphasis"><em>f(x)</em></span> -
      <span class="emphasis"><em>without the need for any derivatives of <span class="emphasis"><em>f(x)</em></span></em></span>.
    </p>
<p>
      The <code class="computeroutput"><span class="identifier">bracket_and_solve_root</span></code>
      functions use <a class="link" href="roots_noderiv/TOMS748.html" title="Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions">TOMS 748 algorithm</a>
      by Al