Tests for the BzzNonLinearSystem Class

Thirty tests were considered, but some of them are the same problem solved with different initial guesses. The Results. txt file contains the results for the tests. The first column univocally identifies the test problem, the second column indicates the number of variables for the corresponding test, the third column shows the number of iterations required to solve the problem, and the fourth column reports the maximum residual  

A set of nonlinear systems typical of chemical engineering was provided in an important paper by Shacham et al. (2002), which also contained several useful recommendations on their solution. The tests are also available at www.polymath-sofiware.com/library. 

We selected the multivariable tests (from 30 to 74). The total computational time required to solve all the 45 tests is less than 0.01 s (minimum value for the clock machine) using an ordinary Dell laptop with Visual C++ 6 and a single processor. 

Test no. 58 has been removed from the list since, as Shacham et al. indicate, no program can solve it due to the discontinuities in its formulation. We will consider this problem separately later (see Caveat no. 3, Section 7.23). 

When the number of equations and variables is quite large, oftentimes each equation depends on a reduced set of variables. Where Newton s and quasi-Newton methods are concerned, the sparsity of the Jacobian matrix has to be exploited to reduce memory allocation while saving on CPU time. The following expedients in 

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