Linear interpolation method

When several parameters need to be optimized simultaneouslyf the use of simple model equations (ifpossible) seems to have advantages over linear interpolation methods. If the required equations become more complicated, however, this advantage is rapidly lost. 

Thirteen AMS C dating samples were obtained from Qinghai sediment core, dates were converted to calendar years before present using IntCal013 (Table 1 and Fig. 2). Then used the linear interpolating method to get the age of each sample, the top age of sediments core was 0, we were used 471 samples to analysis the Holocene climate change of Qinghai Lake. 

The temperature distribution of concrete around the pipe in the initial moments may determined by the value of concrete temperature test before heat storage. Temperature value of node that not installed point for measuring temperature may determined by linear interpolation methods. 

Occasionally it is necessary to identify spectral lines by wavelength measurement. The most common procedure in the analytical spectrochemical laboratory is to use a linear interpolation method based on known wavelengths of nearby lines. Figure 7-1 illustrates this technique, utilizing the known wavelengths of the two copper lines. The upper part of Figure 7-1 is a portion of a spectrum of a sample containing copper (spectral lines 1 and 2)... 

The Method of linear Interpolation (Method of False position)... 

The Method of Linear interpolation (Method of False Position)... 

Linear interpolation method (U.m) This function consists of the same parts as the XGX.m function. The number of input arguments is one more than that of XGX.m, because the linear interpolation method needs two starting points. Special care should be taken to introduce two starting values in which the function have opposite signs. Eq. (1.5) is used without change as the function the root of which is to be located. This function is contained in a MATLAB function called Colebrook.m. 

LI Finds a zero of a function by the linear interpolation method. 

Linear Interpolation method to find one root of a nonlinear equation. 

Let be a well-defined finite element, i.e. its shape, size and the number and locations of its nodes are known. We seek to define the variations of a real valued continuous function, such as/, over this element in terms of appropriate geometrical functions. If it can be assumed that the values of /on the nodes of Oj, are known, then in any other point within this element we can find an approximate value for/using an interpolation method. For example, consider a one-dimensional two-node (linear) element of length I with its nodes located at points A(xa = 0) and B(a b = /) as is shown in Figure 2.2. 

The calculation of (DCFRR) usually requires a trial-and-error solution of Eq. (9-57), hut rapidly convergent methods are avadahle [N. H. Wild, Chem. Eng, 83, 15.3-154 (Apr. 12, 1976)]. For simplicity linear interpolation is often used. 

There may be more than one TS connecting two minima. As many of the interpolation methods start off by assuming a linear reaction coordinate between the reactant and product, the user needs to guide the initial search (for example by adding different intermediate structures) to find more than one TS. 

TABLE 2—Relative errors for DS, FFT-based method and MLMI over different grids (%) (Green, Constant and Bilinear stand, respectively, for the schemes based on Green s function, constant function, and linear interpolation in determining the influence coefficients). ... 

The Galerkin finite element method results when the Galerkin method is combined with a finite element trial function. The domain is divided into elements separated by nodes, as in the finite difference method. The solution is approximated by a linear (or sometimes quadratic) function of position within the element. These approximations are substituted into Eq. (3-80) to provide the Galerkin finite element equations. For example, with the grid shown in Fig. 3-48, a linear interpolation would be used between points x, and, vI+1. 

The higher order ODEs are reduced to systems of first-order equations and solved by the Runge-Kutta method. The missing condition at the initial point is estimated until the condition at the other end is satisfied. After two trials, linear interpolation is applied after three or more, Lagrange interpolation is applied. 

Looking ahead to the issue of solutions, it is important to realize that what is being sought by the solution method is a discrete set of points, x , yj, U(xi, yj), which specify the values of the potentials at the grid locations. To obtain values of the potentials at other jx)ints lying between the sampling locations, other techniques can be employed. Straightforward linear interpolation is one such method that is simple to implement and efficient to compute, but it suffers from a lack of sufficient accuracy required in... 

As it will be discussed, while three maxima of the first derivative are observed, the second one is a consequence of the applied numerical method. Using the second derivative values in the last column, local inverse linear interpolation gives V = 3.74 ml and V = 7.13 ml for the two equivalence points. We will see later on how the false end point can be eliminated. 

---