Linear approximation method for interpolation, Mathematics

Assignment Help:

Linear Approximation Method

This is a rough and ready method of interpolation and is best used when the series moves in predicted intervals. It can be applied to interpolate values in both ascending and descending series. The method can be best described with the help of illustrations.

Example 

The sales in units of a consumer durable are ascertained as follows:

Year

1986

1987

1988

1990

Sales Units (in '000s)

8

16

24

40 

The records of sales for the year 1989 were accidentally lost in a fire. The sales in this year could be interpolated by the following procedure:

  1. Use the value of the immediately preceding year as the base value or starting value. We may connote this as base value.

The year immediately preceding 1989, is 1988. Hence 24,000 units sold in 1988 is the base value.

  1. Ascertain whether the series is an ascending one or a descending one.

In the illustration, since demand for the units is steadily increasing, we may conclude that it is an ascending series.

  1. Find out the difference in values of the variable corresponding to the immediately succeeding and preceding years of the year for which the value is to be interpolated. We may connote this as upper limit minus lower limit.

         Value corresponding to the immediately succeeding year (1990) = 40,000 units

         Value corresponding to the immediately preceding year (1988) = 24,000 units

         Upper limit - Lower limit               = 40,000 - 24,000

                                                       = 16,000

  1. Find out the time interval between the two known values. We may denote this as ts - tp.

         In the above illustration, the time interval between 1988 and 1990 is 2 years.

  1. Find out the time interval between the immediately preceding year and the year for which the value is to be interpolated. We may denote this as ti - tp.

         Time interval between 1988 and 1989 is one year.

  1. Interpolate the value as follows:

         For the illustration, the sales for the year 1989 will be,

24000 +

1008_linear approximatio method.png  x 1

         = 24,000 + 8,000 = 32,000

If the series is a descending series, the formula will be,

Base Value -   1116_linear approximation method1.png  x (ti - tp)              

Related Discussions:- Linear approximation method for interpolation

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Error in measurement, what is actual error and how do you calculate percen...

what is actual error and how do you calculate percentage error

Conditional probability: dependent events, We can define the conditional pr...

We can define the conditional probability of event A, given that event B occurred when both A and B are dependent events, as the ratio of the number of elements common in both A an

High dimensions, List the five most important things you learned about high...

List the five most important things you learned about high dimensions.

Break even point, what is break even point and how can it helps managers to...

what is break even point and how can it helps managers to make decisions?

Find out the slope of equations, Example:  find out the slope of equations ...

Example:  find out the slope of equations and sketch the graph of the line.                         2 y - 6x = -2 Solution To get the slope we'll first put this in slope

Determine the equation of the tangent line, Determine the equation of the t...

Determine the equation of the tangent line to r = 3 + 8 sinθ at θ = Π/6. Solution We'll first need the subsequent derivative. dr/dθ = 8 cosθ The formula for the deriv

How will the decimal point move when 245.398 is multiplied, How will the de...

How will the decimal point move when 245.398 is multiplied by 100? It is moved two places to the right. While multiplying by multiples of 10, the decimal point is moved to the

Statistics, The winning team''s score in 21 high school basketball games wa...

The winning team''s score in 21 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 11.0 points, find the 90% confiden

What is the measure of its width if its length is 3 inches, The perimeter o...

The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width? Let x = the width of the rectangle. Let x + 3 = th

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd