VPM's "Radius Root Finder"

**UWSojourner** · 25th June 2006, 00:49

In Baker's code he uses a search technique"RadiusRootFinder" to solve for the root of a cubic equation with coefficients A, B, C.

Is there a reason not to just solve it analytically? Are there conditions that cause the analytic solution to fail? Kinda new to VPM and was just wondering.

Michael Prange · 25th June 2006, 12:17

Quote: (Originally Posted by UWSojourner)

Is there a reason not to just solve it analytically? Are there conditions that cause the analytic solution to fail?

I'm not familiar with Baker's code, but I am familiar with numerics issues. Often a root finder is used in lieu of an analytical solution because it is faster (involves fewer floating-point operations). A disadvantage of a root finder is that if you don't choose a good starting guess, you may find the wrong root. I suspect that either Baker's algorithm provides a good starting guess, or two of the roots are always complex, so that a root finder which works only with real numbers has only one root to find.

**UWSojourner** · 25th June 2006, 19:24

Quote: (Originally Posted by Michael Prange)

Often a root finder is used in lieu of an analytical solution because it is faster (involves fewer floating-point operations).

That very well may be right. I haven't tested the speed difference, but the limited testing I've done his numeric solution converges in about 3 iterations which is pretty fast.

25th June 2006, 00:49	#1 (permalink)
UWSojourner Pacific Northwest Current Rebreather/s: Megalodon Other Rebreather/s: Join Date: Feb 2005 Location: Portland Oregon Posts: 556	VPM's "Radius Root Finder" In Baker's code he uses a search technique"RadiusRootFinder" to solve for the root of a cubic equation with coefficients A, B, C. Is there a reason not to just solve it analytically? Are there conditions that cause the analytic solution to fail? Kinda new to VPM and was just wondering.
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25th June 2006, 12:17	#2 (permalink)
Michael Prange Michael Prange Current Rebreather/s: Inspiration Vision Other Rebreather/s: Join Date: Mar 2005 Location: Somerville, MA, USA Posts: 10	Re: VPM's "Radius Root Finder" Quote: (Originally Posted by UWSojourner) Is there a reason not to just solve it analytically? Are there conditions that cause the analytic solution to fail? I'm not familiar with Baker's code, but I am familiar with numerics issues. Often a root finder is used in lieu of an analytical solution because it is faster (involves fewer floating-point operations). A disadvantage of a root finder is that if you don't choose a good starting guess, you may find the wrong root. I suspect that either Baker's algorithm provides a good starting guess, or two of the roots are always complex, so that a root finder which works only with real numbers has only one root to find.
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25th June 2006, 19:24	#3 (permalink)
UWSojourner Pacific Northwest Current Rebreather/s: Megalodon Other Rebreather/s: Join Date: Feb 2005 Location: Portland Oregon Posts: 556	Re: VPM's "Radius Root Finder" Quote: (Originally Posted by Michael Prange) Often a root finder is used in lieu of an analytical solution because it is faster (involves fewer floating-point operations). That very well may be right. I haven't tested the speed difference, but the limited testing I've done his numeric solution converges in about 3 iterations which is pretty fast.
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