Quantitive Error Analysis Method For Complex Computation Process And Application

With the widely application of large-scale industry system, large-scale complex computation process has attracted many attentions. Most theoretic results, such as the convergences of computation process, are based on the assumption that the computation process doesn't exist computation error. However because of the express fashion of floating point number, the computation process could exist rounding error everywhere. In most time, the rounding error is very small and will not cause serious inference, which induces few people to pay attention to this field. However, many serious results have knocked back this wrong idea and give us many lessons. So, the computational float rounding error caused by machine error must be widely attentive.We devote to studying the computational rounding error caused by machine error and have held some result, which are shown as follows:◆ Firstly, an automatically quantitative error analysis method is proposed based on interval analysis, which references automatic difference and regards the whole complex computation process as the set composed of a sequence of basic computation, which only includes one basic operation, and we analyze whole complex computation process with interval analysis. Then we write MATLAB Automatic Error Analysis Toolbox, which can automatically analyze the computational rounding error caused by the machine error in any complex computation process. With this MATLAB Toolbox, we analyze the computational rounding error of bombing process in military field for the first time.◆ Secondly, we analyze the rounding error caused by the machine error in iterative algorithms and hold following results: if there existed more rounding off errors, the computation process could be more incorrect. Then we proposed a new iterative algorithm using rounding error bound as second stop criterion instead of iterative time bound, which can adjust the iterativetime bound according to different computation precision. The simulations expound the benefit of this algorithm. Then we analyze the reason caused the failure of rounding off error in traditional Newton algorithm and explain the mechanism: whether the rounding off error influences the convergence character of traditionally iterative convergent algorithm. If not, the rounding off error only affects each iterative value and not the final iterative result. ◆ Thirdly, a new inverse interval matrix method is proposed to deal with the division in multiple dimension computation process. Then MATLAB Automatic Error Analysis Toolbox is extended to analyze the computational rounding error of multiple dimension complex computation process.