J. For. Sci., 2004, 50(9):439-446 | DOI: 10.17221/4639-JFS

Calculus of variations and its application to division of forest land

M. Matějík
Faculty of Forestry and Wood Technology, Mendel University of Agriculture and Forestry, Brno, Czech Republic

The paper deals with an application of the least squares method (LSM) for the purposes of division and evaluation of land. This method can be used in all cases with redundant number of measurements, in this case of segments of plots. From the mathematical aspect, the minimisation condition of the LSM is a standardised condition ∑ pvv = min., minimising the Euclidean norm ||v||E of an n-dimensional vector of residues of plot segments at simultaneous satisfaction of the given conditions. The traditional procedure of calculus of variations with the use of Lagrangian function is shown. If some additional conditions are included in the calculation, on the basis of the criteria presented in this article it is possible to evaluate the degree of deformation of the selected solution in relation to the measured quantities. The application of the method of adjustment of condition measurements may help solve the problems of parcel division on the basis of intersection of the parcel layers according to the real-estate cadastre and according to previous land records, valuation, typological, price and other map sources.

Keywords: area; land; division of land; real-estate cadastre; mean square error; least square method; calculus of variations; adjustment with conditions

Published: September 30, 2004  Show citation

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Matějík M. Calculus of variations and its application to division of forest land. J. For. Sci. 2004;50(9):439-446. doi: 10.17221/4639-JFS.
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    References

    1. ALEXEJEV V.M., TICHOMIROV V.M., FOMIN S.V., 1991. Matematická teorie optimálních procesů. Praha, Academia: 357.
    2. BÖHM J., RADOUCH V., HAMPACHER M., 1990. Teorie chyb a vyrovnávací počet. Praha, GKP, 2.vyd.: 416.
    3. BUMBA J., 1992. Mapy velkých měřítek v České republice. Geodetický a kartografický obzor, 38/80 (12): 253-259.
    4. KUBÁČEK L., 1983. Základy teórie odhadu. Bratislava, Veda: 254.
    5. KUBÁČEK L., KUBÁČKOVÁ L., 2000. Statistika a metrologie. Olomouc, Univerzita Palackého: 307.
    6. KUBÁČEK L., PÁZMAN A., 1979. Štatistické metódy v meraní. Bratislava, Veda: 147.
    7. MÍKA S., 1985. Numerické metody algebry. Praha, SNTL: 169.
    8. PÁZMAN A., 1980. Základy optimalizácie experimentu. Bratislava, Veda: 180.
    9. PELIKÁN J., 2001. Diskrétní modely v operačním výzkumu. Praha, Professional Publishing: 163.
    10. VIŠŇOVSKÝ P., ČIHAL A., 1985. Geodézia a fotogrammetria. Bratislava, Príroda: 546.
    11. ČÚZK, 2001. Návod pro správu a vedení katastru nemovitostí. Praha: 86.

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