APPROXIMATE SEVERAL ZEROS OF A CLASS OF PERIODICAL COMPLEX FUNCTIONS

作者：GAO TA; WANG ZK

来源：Journal of Computational Mathematics, 1990, 8(4): 381-385.

This paper discussed the number of zeroes of the complex function F : C --> C defined by
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where Im(Z) is the imaginary part of Z, \a(n)\ + \b(n)\ not-equal 0. Let n1 = max\1 less-than-or-equal-to k less-than-or-equal-to n {0,k\b(k) not-equal -ia(k)} and n2 = max\1 less-than-or-equal-to k less-than-or-equal-to n {0,k\b(k) not-equal ia(k)}. We prove that if 0 is a regular value of F and n1n2 not-equal 0, then F has at least n1 + n2 zeroes in domain (0,2-pi] x R and n1 + n2 of them can be located with the homotopy method simultaneously. Furtheromore, if alpha-1 = ... = alpha(m) = 0 and n1n2 not-equal 0, then F has exactly n1 + n2 zeroes in domain (0, 2-pi] x R.

• 出版日期1990-10
• 单位中山大学