• THE APPLICATION OF THE COMPUTATION OF MATRICES IN MEASUREMENT ADJUMENT

Abstract

In this paper, we will introduce the application of the decomposition of matrices in measurement. Because of many reasons, not only the immanent causes, but also the external causes, make the results of the measurement in topography not very precise. In order to improve the precision of the measurement result, we need to measure more dates than that we need, which we call them as the redundant measurement, the consequences of these is the inconsistency of the results. then the aim of the measurement adjument is to reduce these errors. In this paper, only the condition adjustment of connecting traverse will be discussed. In order to handle the measurement dates, mathematical model should be built. In connecting traverse, there are three equations, the number of equations are equal to that of the redundant measurement. For the condition adjument, the model of it is linear, but not all measurement problems will cause the adjustment problems, it only appears when we do the redundant measurement. The method of solving this model is the least squares method, usual it is a good method to solve this problem, but when the ill-conditioned matrix arise, such as the coefficient matrix of the normal equation, the inaccuracy of the result will be increased. So a improved singular value decomposition which also combined with the method of distract the error will be introduced to decrease the inaccuracy in this paper.

Keyword: Condition adjustment; Ill-conditioned matrix; The least square method; The truncated singular value decomposition method.

Classification codes: 15A60.