BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
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48 Petronela Paraschiv<br />
interpolate functions φ( x)<br />
have continuous derivates until a random order<br />
(Elias et al., 2004; Tannous et al., 1996; Wagenaar & von Emmerik, 1996).<br />
The interpolation of a discreet set of data [x, y] supposes the<br />
determination of a function f(x) so that f(x) = y, in order to complete the set of<br />
data in any other point x 0 ≠ x 1 . The function f(x) represents the best<br />
approximation of the set of data, in this case not being necessary for the<br />
determined function to pass through all the given points, but it has to be “the<br />
best approximation” after a certain error criterion imposed. Therefore, the<br />
method of the smallest squares gives, for instance, the best approximation in the<br />
sense of minimizing the squre distances from the given points and the<br />
approximation points.<br />
3. Conclusions<br />
1. Applying an interpolation function, linear, spline cubic or polynomial,<br />
for the whole set of data or only for some periods of the values, determines the<br />
interpolation function coefficients so that the interpolation curve to pass through<br />
all given value points.<br />
2. The cubic spline curve is an even curve, defined by a set of<br />
polynomials of the third degree. The curve between each pair of points is a<br />
polynomial of the third degree calculated in such a way as to lead to even<br />
transitions from a polynomial of the third degree to the other.<br />
3. For the situation in which two curves need to be compared, one<br />
experimental given by relative values, and one theoretical given by absolute<br />
values, the interpolation may allow finding a convenient function of<br />
interpolation, the same for both curves to be compared, in which the mathematic<br />
function coefficients differ from ne curve to the other.<br />
4. The interpolation function found needs to satisfy the condition that it<br />
represents the best approximation for any other two curves, experimental and<br />
theoretical, that express the variation of the same physical phenomenon.<br />
REFERENCES<br />
Antonescu D., Buga M., Constantinescu I., Iliescu M., Metode de calcul şi tehnici<br />
experimentale de analiza tensiunilor în biomecanică. Ed. Tehnică, Bucureşti,<br />
1986.<br />
Azar F. M., Calandruccio J. H., Arthroplasty of the Shoulder and Elbow. (Canale, S. T.,<br />
Beaty, J. H., Eds.) Campbell’s Operative Orthopaedics, 11th Ed. Mosby,<br />
Phyladelphia, 2008.<br />
Elias J.J., Wilson D.R., Adamson R., Cosgarea A.J., Evaluation of a Computational<br />
Model Used to Predict the Patellofemoral Contact Pressure Distribution. Journal<br />
of Biomechanics, 37(3), 295-302 (2004).