4.9 Interval Projected Polyhedron algorithm

We illustrated the effectiveness of the IPP algorithm using the single polynomial equation that we used in Example 4.6.2. The output of this computation is listed in Table 4.5. If we compare the bounding boxes of Tables 4.1 and 4.5 for each iteration, we can easily recognize that the bounding boxes of the RIA are always conservative with respect to the FPA. Also at iteration 9, FPA loses the root 0.7 due to floating point error, while RIA finds it.

Iter | Bounding Box (RIA) | Message |

1 | [0, 1] | |

2 | [0.076363636363635, 0.856000000000001] | |

3 | [0.0981877322393447, 0.770083868324001] | |

4 | [0.0999880766853675, 0.723874047810262] | Binary Sub. |

5 | [0.402239977003124, 0.704479954527489] | |

6 | [0.550441290533286, 0.700214508664294] | |

7 | [0.591018492648947, 0.700000534482208] | |

8 | [0.599458794784611, 0.700000000003333] | Binary Sub. |

9 | [0.649998841568894, 0.7] | Root Found |

10 | [0.599997683137788, 0.649998841568895] | Root Found |

11 | [0.0999999994787598, 0.402239977003124] | Root Found |

- 4.9.1 Formulation of the governing polynomial equations
- 4.9.2 Comparison of software and hardware rounding