Numerical Analysis

Archive for January, 2012

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Self-studying calculus?

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I’m young (not that much, not that few) and I’m having problems
at learning at school.
I’m attending the high school, and I’m having most problems with
limits and function continuity.

May someone advice me for a good book about calculus ?

But, often legendary books gets publishied.
Say, the K&R about the C language… Isn’t there anything like the K&R
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non-linear least squares with constraints

Hi,

I have a simple problem where I’m trying to minimize the distance
between a point r0 and a surface or volume (assuming the point r0 is
exterior).  Points in the surface or volume are located by the function
r(L1,L2) for a surface and r(L1,L2,L3) for a volume where
0<=L1,L2,L3<=1.  r maps into (x,y,z) coordinates.

We have black-box routines that do this nicely, but they are too slow
for our purposes, so I have been trying to implement a non-linear least
squares solver that cuts out all the extra unnecessary stuff.  Most of
the references I have found only deal with the unconstrained problem.

For example, I am looking at implementing algorithm 3.16 of

http://www.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf

My questions are

1. How does one restrict these non-linear solvers to work within the
constraits and still be sure you have the optimimum point?  What I am
worried about is that the algorithm could find a minimum point on one of
the boundaries, but if left unconstrained, might wrap around outside the
box to a better point on another boundary.

2. What is the best procedure to keep the solver within the constraint
box? For example, if the solver steps outsides the bounds, do you just
truncate the point to the boundary or possibly start forcing the solver
to take ever smaller steps as you approach boundary?

Thanks,
John

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