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OCR: NONLINEAR SYSTEM SOLVER SAMPLE SCRIPTS Example 1 Solve the system of eauations x2+ y2 = 1 describing the intersection of unit circle with the line y = X This probl lem has two solutions: Starting from (1,1) one expects to obtain the solution (sqrt(2/2 sqrt(2)/2) Starting from -1 the expected result is sqrt(2)/2 sqrt(2)/2) Of course in general one does not know the solutions of the system in advance or many times, whether there are any solutions and if there are solutions how many there are Problem Scripts: Quasi-Newton (see next screen for Brent ) Quasi-Newton: project eqns, solnVector, initVector: local maxlterations xTolerance fTolerance; maxlterations 100; xToler rance fTolerance 0e-6 initVector {1,1} Function eqns(x) y[1] x[1]^ 2+x[2]^2-1; y[2] x[2] x[1]; return end function; solnVecto ...