Basic harness for testing NIST problems.

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+NIST/ITL StRD

+Dataset Name:  MGH09             (MGH09.dat)

+

+File Format:   ASCII

+               Starting Values   (lines 41 to 44)

+               Certified Values  (lines 41 to 49)

+               Data              (lines 61 to 71)

+

+Procedure:     Nonlinear Least Squares Regression

+

+Description:   This problem was found to be difficult for some very 

+               good algorithms.  There is a local minimum at (+inf,

+               -14.07..., -inf, -inf) with final sum of squares 

+               0.00102734....

+

+               See More, J. J., Garbow, B. S., and Hillstrom, K. E. 

+               (1981).  Testing unconstrained optimization software.

+               ACM Transactions on Mathematical Software. 7(1): 

+               pp. 17-41.

+

+Reference:     Kowalik, J.S., and M. R. Osborne, (1978).  

+               Methods for Unconstrained Optimization Problems.  

+               New York, NY:  Elsevier North-Holland.

+

+Data:          1 Response  (y)

+               1 Predictor (x)

+               11 Observations

+               Higher Level of Difficulty

+               Generated Data

+ 

+Model:         Rational Class (linear/quadratic)

+               4 Parameters (b1 to b4)

+ 

+               y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e

+ 

+

+ 

+          Starting values                  Certified Values

+

+        Start 1     Start 2           Parameter     Standard Deviation

+  b1 =   25          0.25          1.9280693458E-01  1.1435312227E-02

+  b2 =   39          0.39          1.9128232873E-01  1.9633220911E-01

+  b3 =   41.5        0.415         1.2305650693E-01  8.0842031232E-02

+  b4 =   39          0.39          1.3606233068E-01  9.0025542308E-02

+

+Residual Sum of Squares:                    3.0750560385E-04

+Residual Standard Deviation:                6.6279236551E-03

+Degrees of Freedom:                                7

+Number of Observations:                           11

+ 

+ 

+

+

+

+

+

+ 

+ 

+ 

+Data:  y               x

+       1.957000E-01    4.000000E+00

+       1.947000E-01    2.000000E+00

+       1.735000E-01    1.000000E+00

+       1.600000E-01    5.000000E-01

+       8.440000E-02    2.500000E-01

+       6.270000E-02    1.670000E-01

+       4.560000E-02    1.250000E-01

+       3.420000E-02    1.000000E-01

+       3.230000E-02    8.330000E-02

+       2.350000E-02    7.140000E-02

+       2.460000E-02    6.250000E-02