Large amounts of computer time and storage requirements can be used when performing least squares adjustments. This is due to the fact that as the problems become more complex, the matrices become larger, and the storage requirements and time consumed in doing numerical operations grow rapidly. As an example, in analyzing the storage requirements of a 25-station horizontal least squares adjustment that has 50 distance and 50 angle observations, the coefficient matrix would have dimensions of 100 rows and 50 columns. If this adjustment were done in double precision,1 it would require 40,000 bytes of storage for the coefficient matrix alone. The weight matrix would require an additional 80,000 bytes of storage. Also, at least two additional similarly sized intermediate matrices2 must be formed in computing the solution. From this example, it is easy to see that large quantities of computer time and computer memory can be required in least squares adjustments. Thus, when writing least squares software, it is desirable to take advantage of some storage and computing optimization techniques. In this chapter, some of these techniques are described.
26.2 STORAGE OPTIMIZATION
Many matrices used in a surveying adjustment are large but sparse. Using the example above, a single row of the coefficient matrix for a distance observation would require a 50-element row for its four nonzero elements. In fact, the entire coefficient matrix ...