DOI: 
10.22389/0016-7126-2022-980-2-57-62
1 Gerasimenko M.D.
Year: 
№: 
980
Pages: 
57-62

Institute of applied mathematics FEB RAS

1, 
Abstract:
It is shown that an increase in the number of significant digits in calculations does not always lead to an increase in the accuracy of the final calculations, and it is impossible to judge in advance the required number of significant digits in calculations. It is necessary to distinguish between the conditionality of the task and that of its solution method, since solving of a well-posed task can be spoiled by an incorrectly chosen algorithm. A crucial role in overcoming this problem is played by the applied computational. Reliably obtaining the inverse or pseudo-inverse matrix of a given accuracy does not also guarantee the same accuracy of obtaining the necessary unknowns. The inversion or pseudo-inversion of a ill-conditioned matrix can lead to an unexpected, absurd result. The solution of this matter is very important, for example, at determining the parameters of an earthquake source in real time, as well as adjusting the planned networks with measured bases and azimuths as input data, which are given high measurement weights.
The work was carried out within the framework of the state task of the FSBI Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of Sciences.
References: 
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Citation:
Gerasimenko M.D., 
(2022) Problems in solving ill-conditioned normal equations. Geodesy and cartography = Geodezia i Kartografia, 83(2), pp. 57-62. (In Russian). DOI: 10.22389/0016-7126-2022-980-2-57-62
Publication History
Received: 18.04.2021
Accepted: 31.01.2022
Published: 20.03.2022

Content

2022 February DOI:
10.22389/0016-7126-2022-980-2