| The present investigation deals with the reliability of the data, intermediate parameters and final results concerning the design, observation and computation of a local high precision network.; Nowadays precision, rigour, quality definitively is highly demanded.; Precision concept is fundamental in any geodetic work and, joined with reliability and cost, define the three fundamental parameters in any geodetic action (Nunez et al. 1991).; It can be defined reliability as the capacity of a network to detect gross errors in the observations. (Nunez et al. 1991).; So it is necessary to check the error figures and computation algorithms, included the numerical rounding errors introduced by the successive arithmetic operations of the computer, which play an important role.; An important part of the investigation is devoted to the resolution of a least-squares equations system as an example Ax-K=R (where A is the design matrix, K the independent terms vector and R the residuals vector), both free network or tie, where it can be found that the matrix S=ATPA is highly sensitive to any rounding operation, resulting in a great discrepancies in the solution vector of the unknowns X.; This sensibility is inevitable and could become a grave inconvenient in the final results of a network with highly levels of precision and rigour demanded, such as deforming networks.; However, before to decide the observation repetition, probably with a new methodology and another instrumentation, we can improve the situation with some new calculation procedure.; Main topics of the investigation are: (1) Error boundaries in S and b=ATPK. (2) Matrix inverse alternatives. (3) Consideration about all the information available in the covariance matrix through a new error figures. (4) Error figures about observables. (5) Lineal system equations generation with exact design matrices which avoid the rounding errors.; These are the principal aspects to be treated in the present investigation entitled: "Contribution to the high precision local networks general problem: specific theoretician and practical conditions of judgement, intermediate parameters qualifications and final results". |
