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87     * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
94 * <code>a := initial -1; b := initial +1,</code> examines the value of the
109 * near <code>initial,</code> it is better to use
114 * @param initial initial midpoint of interval being expanded to
123 * is not positive, or initial is not between lowerBound and upperBound
126 double initial, double lowerBound, double upperBound)
128 return bracket( function, initial, lowerBound, upperBound,
134 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
141 * <code>a := initial -1; b := initial +1,</code> examines the value of the
152 * @param initial initial midpoint of interval being expanded to
163 * is not positive, or initial is not between lowerBound and upperBound
166 double initial, double lowerBound, double upperBound,
177 if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) {
180 lowerBound, initial, upperBound);
182 double a = initial;
183 double b = initial;
201 numIterations, maximumIterations, initial,