A textbook of Computer Based Numerical and Statiscal Techniques part 3. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 6 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES implies that 5X n5x1 or 5x1 3x1 . dX . dX X Using the principle of equal effects which states 5x1- 5x2- . 5xn--- this 3x1 3x2 dxn 5X . 5X _ 5X dX Similarly we get 5x2 y 5x3 X . n n----- n--------- 3x1 dx2 dx3 5 _ 5X 5xn dX and so on. n---- dXn This form is useful where error in dependent variable is given and also we are to find errors in both independent variables. Remark The Error 1 1C-n if a number is correct to n decimal places. Also Relative error is less than - 4 if number is correct to n significant digits and l is the first significant digit of a number. Error in Evaluating X Let xk be the function having k is an integer or fraction then Relative Error for this function is given Relative Error 5x k or x 5X X 5x x Example 2. Find the absolute percentage and relative errors if x is rounded-off to three decimal digits. Given x . Sol. If x is rounded-off to three decimal places we get x . Therefore Error True value - Approximate value Error .005998 - .006 - .000002 Absolute Error Ea Error Relative Error Er ----E E and r True value Percentage Error Ep Er x 100 . Example 3. Find the number of trustworthy figure in 3 assuming that the number is correct to last figure. Sol. We know that Relative Error Er 5X k 5x X x 1 Here 5x because x 10 3 2 ERRORS AND FLOATING POINT 7 8x 3 x or k 3 x---------5- --------- x 3 Therefore Absolute Error or Absolute Error x 3 x The error affects the third decimal place therefore 3 is correct to second decimal places. 1 Example 4. If is the approximate value of -3 then find its absolute relative and percentage errors. 1 Sol. Given that True value x v 7 3 and its Approximate value X Therefore Absolute Error Ea X - X 1 3 - Relative Error E .
