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FIBONACCI SEARCH
99
So the range is reduced to
Iteration 3. We compute
The range is reduced to
Iteration 4. We choose e = 0.05. We have
The range is reduced to Note 63 - a4 = 0.275 < 0.3. For the diligent reader, we now turn to a proof of the optimality of the Fibonacci search method. Skipping the rest of this section does not affect the continuity of the presentation. To begin, recall that we wish to prove that the values of p\, p2,..., PN used in the Fibonacci method, where pk = 1 — FM-k+\IFN-k+i* solve the optimization problem:
99
So the range is reduced to
Iteration 3. We compute
The range is reduced to
Iteration 4. We choose e = 0.05. We have
The range is reduced to Note 63 - a4 = 0.275 < 0.3. For the diligent reader, we now turn to a proof of the optimality of the Fibonacci search method. Skipping the rest of this section does not affect the continuity of the presentation. To begin, recall that we wish to prove that the values of p\, p2,..., PN used in the Fibonacci method, where pk = 1 — FM-k+\IFN-k+i* solve the optimization problem:
