Resumo
The author proves that equation, Σy n ΣZx | ΣxyZx ΣxZx ΣxZ2x | = 0, Σy ΣZx Σy2x | where Z = 10-cq and q is a numerical constant, used by Pimentel Gomes and Malavolta in several articles for the interpolation of Mitscherlih's equation y = A [ 1 - 10 - c (x + b) ] by the least squares method, always has a zero of order three for Z = 1. Therefore, equation A Zm + A1Zm -1 + ........... + Am = 0 obtained from that determinant can be divided by (Z-1)³. This property provides a good test for the correctness of the computations and facilitates the solution of the equation.
Assistente Substituto de Matemática da E. S. A. "Luiz de Queiroz"
ABSTRACT
The author proves that equation,
Σy n ΣZx |
ΣxyZx ΣxZx ΣxZ2x | = 0,
Σy ΣZx Σy2x |
where Z = 10-cq and q is a numerical constant, used by Pimentel Gomes and Malavolta in several articles for the interpolation of Mitscherlih's equation
y = A [ 1 - 10 - c (x + b) ]
by the least squares method, always has a zero of order three for Z = 1. Therefore, equation
A Zm + A1Zm -1 + ........... + Am = 0
obtained from that determinant can be divided by (Z-1)3.
This property provides a good test for the correctness of the computations and facilitates the solution of the equation.
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Full text available only in PDF format.
BIBLIOGRAFIA CITADA
- PIMENTEL GOMES, Frederico e Euripedes MALAVOLTA - Considerações Matemáticas sobre a Lei de Mitscherlich. Piracicaba, 1949.
- NOGUEIRA, Izaias Rangel - A Técnica da resolução das equações Relativas à Interpolação da lei de Mitscherlich, pelo Método dos Quadrados Mínimos.
Sôbre uma propriedade da equação utilizada para interpolação da Lei de Mitscherlich
Datas de Publicação
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Publicação nesta coleção
06 Nov 2012 -
Data do Fascículo
1950
