Retųjų matricų formavimas pagal grafų teorijos principus, išlyginant geodezinius tinklus mažiausiųjų kvadratų metodu

Abstract

The article deals with the use of sparse matrices for adjustment of geodetic networks. Sparse matrices have an advantage (against the full matrices) of not keeping the zero elements of the matrices during calculations. This causes savings in computer memory and proceeding time. The identity matrix, if the 1st order GPS network of Lithuania, is given as an example. The example shows that full matrix of size 156 by 495 elements would need 617760 bytes of computer memory, while the same matrix, converted to sparse format, needs only 13716 bytes. The sparse matrices may be used more effectively when the density of non-zero elements is lower. The Matlab software is suggested as one of the possible programming packages for dealing with sparse matrices. The Matlab makes sparse matrix by taking the non-zero elements indexed with row and column numbers. As Matlab treats sparse matrices in the same way as full matrices, the main problem in creation sparse matrices is to find the most effective method of indexing non-zero elements. The sample programming code for making indices of non-zero elements is presented in the article. The code was developed according to the algorithm, based on graph theory for numbering the nodes and vertices of the graph (particularly the geodetic network). This code may help scientists, who are experimenting with adjustment of geodetic networks of large size, to start with indexing of network’s nodes.