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Unformatted text preview: Numerical Analysis II Dr Abigail Wacher Nov 4, 2010 1 Errors Errors can be introducted in several ways. We can have experimental errors (such as measurement errores), machine/computer errors, mathematical approximations. Mathematical approximations, and computer errors can be due to roundoff, truncation, ill-conditioning. Definition If x * is an approximation to x , then x K x * is called the absolute error. and if x s 0, then x K x * x is the relative error. If f : a , b / = is approximated by f ~ : a , b / = then the difference f K f ~ is the truncation error. Depending on how you calculate expressions you could face both rounding errors and truncation errors. To understand this we need to understand the difference between "exact" arithmetic and computer arithmetic. Most applications use real numbers, a continuum in space and/or time. This system has a corresponding system on the computer we call floating point arithmetic....
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