A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx

... Approximate value (x′) = 0 .33 3 Therefore, Absolute Error, 1 0 .33 3 0 .33 333 3 0 .33 3 0.00 033 3 3 a Exx ′ =− =− = − = Relative Error, E r = 0.00 033 3 0.000999 0 .33 333 3 a E x == and Percentage Error, E p = ... second decimal places. Example 4. If 0 .33 3 is the approximate value of 1 3 , then find its absolute, relative and percentage errors. Sol. Given that True val...

Ngày tải lên: 04/07/2014, 15:20

... problems. A major advantage for numerical technique is that a numerical answer can be obtained even when a problem has no analytical solution. However, result from numerical analysis is an approximation, in ... significant figures at each step of computation. At each step of computations, retain at least one more significant figure than that given in the data, perform the last...

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... obtained by x 1 = 2 22 44 and 22 bb ac bb ac aa −+ − −− − =x These are called closed form solution. Similar formulae are also available for cubic and biquadratic polynomial equations but we rarely ... 26 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction, multiplication, and divi...

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... 122 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 22. Evaluate: ∆ n [sin (ax + b)] Sol. We know f∆ (x) = f(x + h) – f (x) therefore ∆ sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... hD hD hD 116 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 14. Evaluate the following: I. ∆ 2 (cos 2x) II. ∆ 2 (3e x ) III. ∆ tan –1 x IV. ∆(x + cos x) the inte...

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... 22 1 2 n nn an bn c n a n b n a n  − −++−∆+∆+∆   142 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 9. Evaluate the production of wool in the year 1 935 from the given data: ( ) 1 931 1 932 1 933 ... given a set of equidistant values of arguments and its corresponding value of f(x). Suppose for n + 1 equidistant argument values x = a, a + h, a + 2h,...

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... R.H.S. 3. 9 FACTORIAL NOTATIONS The product of n consecutive factors each at a constant difference and the first factor being x is called a factorial function or a factorial polynomial of degree n and ... n C 3 x 3 E 3 + ]u 0 = u 0 + n C 1 u 1 x + n C 2 u 2 x 2 + n C 3 u 3 x 3 + = L.H.S. 150 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES CorCor...

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... the Lagrange’s formula is y x = ()()() ()() () ()()() () ()() 53 335 535 5 3 5 3 55 35 33 35 xxx xxx yy −− +−− +−− + −+ −− −− −+ −− −− + ()()() ()()() ()()() ()()() 35 535 533 533 335 55 535 3 xxx ... using Lagrange’s interpolation formula. Sol. We are given () :78910 :31 1 9 x fx 226 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 1. Using Lagrange’s f...

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... life. [Ans. 15.67] 13. Find the value of tan 33 ° by Lagrange’s formula if tan 30 ° = 0.5774, tan 32 ° = 0.6249, tan 35 ° = 0.7002, tan 38 ° = 0.78 13. [Ans. 0.64942084] 14. Apply Lagrange’s formula to ... n ax ax ax ax −− −− 11. Certain corresponding values of x and log 10 x are given as 10 : 30 0 30 4 30 5 30 7 log : 2.4771 2.4829 2.48 43 2.4871 x x Find the log 10 30 1...

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... co-efficients a 1 , a 2 a n will produce little error for small x near zero. But probably substantial error near the ends of the interval 268 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 7. Apply ... approximation to a given function. For evaluating a function f(x) on a computer it is generally more efficient of space and time to have an analytic approxi...

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... 0.5 230 cm. and a standard deviation of 0.0 032 cm. Calculate the 2-sigma and 3- sigma upper and lower control limits for mean of sample of 4. Ans. 2–sigma UCL 0.5262 cm LCL 0.5198 cm CL 0.5 230 ... concern has an average sale of Rs. 10000/- daily estimated over a long period. A salesman claims that he will increase the average sales by Rs. 700/- a day. The concern is...

Ngày tải lên: 04/07/2014, 15:20