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| | Abstract | | It is very important to use precise Jacobian for inversion of geophysical data and sensitivity analysis. Because the result of inversion is strongly affected by the precision of Jacobian. However numerical differences are often used instead of numerical derivatives in most cases. Mathematics using the hyperreal number that is called Non-standard Analysis was investigated by A. Robinson. Using hyperreal number, a derivative of function can be calculated without a limit in mathematics. A new algorithm to calculate partial derivatives precisely using hyperreal number was developed. The result of numerical examples using hyperreal number is presented in this paper. |
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