Spline, cubic, definition

M64 Function value, derivatives and definite integral of a cubic spline at a given point 6400 6450... 

REM J FUNCTION VALUE, DERIVATIVES AND DEFINITE t 4484 REN t INTEGRAL OF A CUBIC SPLINE AT A GIVEN -POINT t 4484 REN lltltllllltmillltlllltllltltllllllltltlllllttltll 4488 REN INPUT ... 

Spline Fitting in One Variable. By definition, a cubic spline function in one variable consists of a set of polynomial arcs of degree three or less joined smoothly end to end. The smoothness consists of continuity in the function itself and in its first and second derivatives. 

Figure 7.9 Geometric definition od a cubic spline in a 2D space.

We call this function a cubic spline on A. The definition of such a function requires a knowledge of the intermediate slopes ... 

The importance of the weight function is obvious from the definition of In fact, the value of the function in every node of the domain is the weighting sum of its values in the rest of the nodes of the star. Various weighting functions are used in practice. The exponential function w x,y) = exp (—10(x + y )) and the cubic spline function are only two examples. Weight functions usually have a compact support. 

The pressure values from the previous time step were represented by a natural cubic spline (IMSL-ICSICU), then integrated (IMSL-DCSQDU) and the values of the interal at various X-locations were themselves represented as a natural cubic spline (ISML-ICSICU). Thus, the values of the definite integral involving the pressure values from the previous time step were available to the function subroutine of DGEAR at any X-location using a cubic spline interpolation (IMSL-ICSEVU),... 

The heat capacities of LUCI3 measured experimentally and smoothed by a cubic spline function were reported by Tolmach et al. (1987c). We calculated 6r>, 6 1, 0e2, 0e3, and a on the basis of all these experimental data, except three values in the temperature range 254.24-262.41 K. The characteristic parameters listed in Table 22 were obtained at a comparatively low = 0.05497 value. Comparison with the corresponding data on hexagonal lanthanide trichlorides shows that an increase in the molar volume causes an insignificant decrease in a, noticeable increases in 0 2 and 0E3, and substantial decreases in 0 and 0ei- Such modifications of these parameters change the temperature dependence of heat capacity in a quite definite way. Namely, because of the low 0 and 6ei values, heat... 

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