[MATH-636] create solvers for Dfp based function

• Type: New Feature
• Status: Closed
• Priority: Major
• Resolution: Fixed
• Fix Version/s: 3.0
• Assignee: Luc Maisonobe
• Reporter: Luc Maisonobe
• Created: 29/Jul/11 09:29
• Updated: 24/Mar/12 16:17
• Resolved: 29/Jul/11 15:48

Description

When validating some regular computations, we often end up doing some comparison with higher accuracy reference data.
The Dfp package is a wonderful tool for that. This package can already be used in some of our regular algorithms as it already implements the Field interface. However, Dfp instances cannot be used in solvers yet.

Setting up solvers that would take Field based function is not possible, as solvers do need an absolute value method to check convergence, and an ordering relation for bracketing. However, no such restriction exist for Dfp.

It is very easy to convert some existing solvers to have a Dfp version. As the main purpose is high accuracy, and as implementing function for Dfp is cumbersome, a high order method using function values only and no need for implementing derivatives such as depicted in MATH-635 is a good choice.