Elements of the Computing Theory

This chapter is devoted to the further development of the theory of computational errors, namely, the work proposes a combined approach to assessing the quality of the solution of the problem. This takes into account the various sources of error that accompany the real computational process. These are first of all method errors, irreversible error, and rounding error. With regard to rounding error, it should be noted that due to the complexity of the tasks to be solved, the number of operations increases significantly, and in some cases, the assessment of rounding error becomes the main one. Ignoring rounding errors means that computer models may have nothing to do with physical ones. Ways to reduce rounding errors are to select the parameter S. The meaning of this parameter is that S memory cells are allocated to one number. Thanks to the parameter S you can adjust the accumulation of rounding errors. This combined approach to assessing the quality of the solution of the problem is a guarantee of the quality of its solution. Failure to take into account at least one component of the error does not provide such a guarantee.