Method and apparatus for initializing interval computations through subdomain sampling

A computer-readable storage medium storing instructions that when executed by a computer system cause the computer system to use a computer system to evaluate a function within a domain using an interval computing technique, the method comprising:

• receiving the function and the domain over which the function is to be evaluated;
• creating a set of sampling subdomains within the domain by generating a set of boxes of different sizes which are located at different positions across the domain;
• performing evaluations on the set of sampling subdomains to generate evaluation results;
• sorting the evaluation results based on box size;
• selecting a box size from the different box sizes by identifying a largest box size which achieves tight bounds on the evaluation results;
• discretizing the domain into subdomains of the selected box size;
• and
• using the interval computing technique to evaluate the function on each of the subdomains wherein the interval computing technique recursively subdivides and evaluates the function on the subdomains.

An apparatus that uses a computer system to evaluate a function within a domain using an interval computing technique, the apparatus comprising:

• a receiving mechanism configured to receive the function and the domain over which the function is to be evaluated;
• a memory for storing the function and the domain;
• a generation mechanism configured to create a set of sampling subdomains within the domain by generating a set of boxes of different sizes which are located at different positions across the domain;
• an evaluation mechanism configured to perform evaluations on the set of sampling subdomains to generate evaluation results;
• a sorting mechanism configured to sort the evaluation results based on box size;
• a selection mechanism configured to select a box size from the different box sizes by identifying a largest box size which achieves tight bounds on the evaluation results;
• a discretization mechanism configured to discretize the domain into subdomains of the selected box size;
• and
• an evaluation mechanism configured to use the interval computing technique to evaluate the function on each of the subdomains by recursively subdividing and evaluating the function on the subdomains.