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with a set of arbitrary initial values in newton method the system of equations don't have any answer. Does it mean that this system of equation don't have any answer at all or may be there exists a set of initial values for which this set has answer? If it is true, how can I find this set of appropriate initial value?

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ARe you asking about the meaning of a sentence you found written down somewhere? If so, please provide more than one context. If not, what do you mean by "with a set of arbitrary initial values"? Do you mean that such-and-such holds for every set of initial values, or just that you have found an initial value with such-and-such property? And how does whether the equation have a solution even depend on how you search for it? Either there's a solution or there's not (if it's there you may or may not be able to find it, but that's different from whether a solution exists). –  Henning Makholm Sep 28 '12 at 14:58
    
No I wrote a program in which I used the newton method for solving 7 nonlinear equations. For many sets of initial values that I try, the equations don't have answer. I want to know that can I find a set of initial values for which this set of equation has answer and if it is true, How can I find this set of initial value? –  soodeh Sep 28 '12 at 16:08

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