Page 113 - Excel for Scientists and Engineers: Numerical Methods

90 EXCEL: NUMERICAL METHODS

function. But instead of actually entering values of the square and the cube of the
x values, you can use an array constant in an array formula, thus
{=TREND(C19:C22,AI 9:A22/\{ 1 ,2,3),FgA{ 1,2,3}, I)}
This example of using the TREND function is found in folder 'Chapter 05
Interpolation', workbook 'Interpolation 1', sheet Cubic Interpolation').

Linear Interpolation in a Two-way Table
by Means of Worksheet Formulas
To perform linear interpolation in a two-way table (a table with two ranges of
independent variables, x and y and a two-dimensional array of z values forming
the body of the table), we can use the same linear interpolation formula that was
employed earlier. Consider the example shown in Figure 5-15; we want to find
the viscosity value in the table for x = 76"F, y = 56.3 wt% ethylene glycol. The
shaded cells are the values that bracket the desired x and y values.

Figure 5-15. Linear interpolation in a two-way table.
The shaded cells are the ones used in the interpolation.
(folder 'Chapter 05 Interpolation', workbook 'Interpolation 11', module ' Linear Interpolation 2-Way')

We must perform three linear interpolations. First, as shown in Figure 5-16,
for the two bracketing values of x we calculate the value of z at y = 56.3. The
formula used in cell 832 is
=lnterpL(0.563,$E$3:$F$3, El 1 :F11)