path—a foundation of file based i o

... proportion of the population Due to the tremendous limitations of time, budget Joint Stock Commercial Bank for Foreign Trade of Vietnam Vietnam Joint Stock Commercial Bank for Private Enterprises ... brand differentiation, brand promise and trust and credibility were found significant in relation with only either rational evaluation or emotional evaluation The different weights of the relationships ... associations will be discussed in details in the below 2.3.1 Brand associations 2.3.1.1 Rational associations Though the product quality is a component of the original model of CBBE; however, banking...

Ngày tải lên: 06/11/2012, 15:52

... contains a systematic collection of orthopaedic findings, which is recommended in occupational medicine for the timely recognition of suspicious findings for avoiding excessive or inappropriate ... prevention program (use of low tech ergonomic aids, back school) 3Treatment in a rehabilitation program for back disorders, consultation with the facility physician 2Participation respect to duration ... manuscript Additional material 15 16 17 18 Additional file 19 Diagnostic procedure of orthopaedic examination Scheme for the orthopaedic examination performed in this study according to Grifka...

Ngày tải lên: 20/06/2014, 00:20

... PROGRAMMING IN ‘C’ LANGUAGE 13.34 ALGORITHM FOR FITTING A STRAIGHT LINE OF THE FORM Y = a + bX Step Start of the program for fitting straight line Step Step Input the number of terms observe Input ... value of x for Which you want the value of y – 9.0 When x = 9.0, y = 810.00 Press enter to exit 13.28 ALGORITHM FOR TRAPEZOIDAL RULE Step Start of the program for numerical integration Step Input ... #include #include float sim(float); void main() { float res, a, b, h, sum; int i, j, n; 601 602 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES clrscr ( ); printf(“Enter...

Ngày tải lên: 04/07/2014, 15:20

... reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of ... difficulty to understand the subject A unique feature of this book is to provide with an algorithm and computer program in Clanguage to understand the steps and methodology used in writing the program ... authors wish to express their thanks to New Age International (P) Limited, Publishers and the editorial department for the inspiration given by them to undertake and complete this project AUTHORS...

Ngày tải lên: 04/07/2014, 15:20

... using high precision computing aids and by correcting obvious errors in the data Round-off Error: The round-off error is the quantity, which arises from the process of rounding off numbers It ... figures since zeros only help to fix the position of the decimal point Similarly, in the number 0.0002070, the first four ‘0’s are not significant figure since they serve only to fix the position of ... desired is known as rounding off a number or we can say that process of dropping unwanted digits is called rounding-off Number are rounded-off according to the following rules: To round-off the...

Ngày tải lên: 04/07/2014, 15:20

... Example 26 How accurately should the length and time of vibration of a pendulum should be measured in order that the computed value of g is correct to 0.01% Sol Period of vibration T is given by ... 12 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Example 20 It is required to obtain the roots of X2 – 2X + log10 = to four decimal places To what accuracy should log10 be given? Sol Roots ... estimate the percentage error in computing the discharge Sol Given that Q = kH5/2 On taking Log both the sides of the equation, we have log Q = log k + log H On differentiating, we get δQ δH = Q H...

Ngày tải lên: 04/07/2014, 15:20

... 90 is correct to one figure only The error due to loss of significant figures sometimes renders the result of computation worthless Using techniques below can minimize such error: (1) a − b by ... using + x2 Taylor’s series expansion about x = Find a bound on the truncation error [Ans 0.25] 13 Obtain a second-degree polynomial approximation to the function f(x) = 14 Find the number of ... FLOATING POINT The IEEE floating-point standards prescribe precisely how floating-point numbers should be represented, and the results of all operations on floating point numbers There are two...

Ngày tải lên: 04/07/2014, 15:20

... Sol Here mantissa is 0.5872 and the exponent is Also shifting of the mantissa to the left to its most significant digit, is nonzero, is called normalization 1.8.1 Arithmetic Operations on Floating ... multiplied by multiplying the mantissa and by adding the exponent of given normalized floating-point representation Similarly division is evaluated by division of mantissa of the numerator by ... 0.1823e3] 33 ERRORS AND FLOATING POINT 10 Give example to show that most of the laws of arithmetic fail to hold for floating-point arithmetic 11 Find the root of smaller magnitude of the equation x2 +...

Ngày tải lên: 04/07/2014, 15:20

... which is positive Therefore f(0.688) is obtained positive, while f(0.625) is negative Therefore, the root lies between 0.625 and 0.688 Fifth approximation: The fifth approximation to the root is ... is negative Therefore f(0.75) is positive, while f(0.625) is obtained negative Therefore, the root lies between 0.625 and 0.75 Fourth approximation: The fourth approximation to the root is given ... 0.023, which is positive Therefore f(0.665) is positive and f(0.657) is negative so that the root lies between 0.657 and 0.665 Eighth approximation: The eighth approximation to the root is given...

Ngày tải lên: 04/07/2014, 15:20

... rate) of convergence of false i →∞  e k   i  position method is 1.618 Example Find a real root of the equation f(x) = x3 – 2x – = by the method of false position up to three places of decimal ... xi − xi −1 < ε, where ε is the prescribed accuracy 2.5.2 Order (or Rate) of Convergence of False Position Method The general iterative formula for False Position Method is given by xi +1 = xi ... root is given by xi −1 f ( xi ) − xi f ( xi −1 ) f ( xi ) − f ( xi −1 ) xi + = 2.5.1 Procedure for the False Position Method to Find the Root of the Equation f (x) = Step 1: Choose two initial guess...

Ngày tải lên: 04/07/2014, 15:20

... of iteration method is In other words, iteration method converges linearly Example Find a real root correct upto four decimal places of the equation 2x – log10 x – = using iteration method Sol ... method of Falsi Position [Ans 0.852605] Apply Falsi Position method to find smallest positive root of the equation x – e–x = correct to three decimal places [Ans 0.567] Find the real root of the ... Rate of Convergence of Iteration Method Let f(x) = be the equation which is being expressed as x = g(x) The iterative formula for solving the equation is xi +1 = g(xi) If a is the root of the...

Ngày tải lên: 04/07/2014, 15:20

... Procedure for Newton Raphson Method to Find the Root of the Equation f (x) = Step 1: Take a trial solution (initial approximation) as x0 Find f(x0) and f ′(x0) Step 2: Find next (first) approximation ... 1.44 correct to two decimal places Similarly, PROBLEM SET 2.3 Use the method of Iteration to find a positive root between and of the equation xex – [Ans 0.5671477] Find the Iterative method, the ... derived from Taylor’s series as follows: Let f(x) = be the equation for which we are assuming x0 be the initial approximation and h be a small corrections to x0, so that f(x0 + h) = Expanding it...

Ngày tải lên: 04/07/2014, 15:20

... ALGEBRAIC AND TRANSCENDENTAL EQUATION Since, imaginary roots occur in conjugate pairs roots are 1.915 ± 1.90 8i upto places of decimal Assuming other pair of roots to be α ± i , then  α + i β + ... Regula-Falsi method, the Secant iteration does not bracket the root and it is not even necessary to bracket the root to start the iteration Hence, it is obvious that the iteration may not always coverage ... The constant k is determined from (6), and it is given by k = cp/(p+1) The convergence of the secant method is superlinear The purpose of this document is to show the following theorem: Roots of...

Ngày tải lên: 04/07/2014, 15:20

... defaulted polynomial Another quadratic factor is of obtained using this default polynomial If the initial approximation of p and q are not known then the last three terms of given polynomial an – ... quadratic factor from polynomial given by equation (1), which gives a pair of complex roots or a pair of real roots Let us divide the given polynomial pn(x) by a quadratic factor x2 + px + q, we obtain ... METHOD This method can also used to determine the both real and complex root of equation f(x) = Let xi–2, xi–1, xi be three distinct approximations to a root of f(x) = and let yi–2, yi–1, yi be...

Ngày tải lên: 04/07/2014, 15:20

... this method is that additional computation is also necessary This method can be applied to find the complex roots and multiple roots of polynomials and also for determining the Eigen values of ... trigonometric functions in terms of simple arithmetic operations 3.2 FINITE DIFFERENCES Numerical methods are very important tools to provide practical methods for calculating the solution of problems ... equal or unequal The study of finite difference calculus has become very important due to its wide variety of application in routine life It has been originated by Sir Issac Newton It has been of...

Ngày tải lên: 04/07/2014, 15:20

... 3.4.4 Other Difference Operators (a) The Operator E: The operator E is called shift operator or displacement or translation operator It shows the operation of increasing the argument value x by its ... of simultaneous increments of mutually dependent quantities where as in differential calculus, we find the limit of such ratios when the increment tends to (c) The Unit Operator 1: The unit operator ... function y = f(x) is defined by Df ( x ) = d f ( x) dx d2 f ( x) and so on dx2 The operator ∆ is an analogous to the operator D of differential calculus In finite differences, we deal with ratio...

Ngày tải lên: 04/07/2014, 15:20

... + ) 119 CALCULUS OF FINITE DIFFERENCES Example 19 Evaluate ∆n eax+b; where the interval of differencing taken to be unity? Sol Given ∆n eax+b; which shows that f(x) = eax+b Now ∆f (x) = f(x + ... CALCULUS OF FINITE DIFFERENCES (E − 2E + 1) sin( x + h ) sin( x + h ) = (E – + E–1) sin (x + h) +  sin( x + h) − sin( x + h ) + sin( x + h )  = [sin (x + 2h) – sin (x + h) + sin x] +   sin( x ... 2sin(x + 2h)[cos h − 1] sin(x + 2h) = sin (x + h) [cos h – 1] + = (cos h – 1) {sin (x + h) – 1}  1 Example 16 Show that B(m + 1, n) = (–1)m ∆m   where m is a positive integer  n ∞ ∫e Sol...

Ngày tải lên: 04/07/2014, 15:20

... with the order of differences The coefficients of δ’s are binomial coefficients with alternative signs +, –, In various difference columns of the above table the algebraic sum of the errors is ... zero., The errors in the column ∆iy are given by the coefficients of the binomial expansion (1 –δ )i In even differences columns of ∆2y, ∆4y, ., the maximum error occurs in a horizontal line in ... degree of original polynomial Again, on taking a difference of equation (2) i. e second difference of equation (1), we get ∆ f ( x) = C2 + C3 x + C4 x + + n(n − 1)h2 an x n −2 …(3) This is a polynomial...

Ngày tải lên: 04/07/2014, 15:20

... using yx in it Such methods of operations are known as method of separation of symbols Point to be noted that the operations on symbols has no meaning without operand yx i. e., yx+nh = Enyx = (1 ... by solving these two we get the two missing values for given function f(x) Similarly method proceeds to find three and more missing terms in given function f(x) Example Estimate the missing term ... 137 CALCULUS OF FINITE DIFFERENCES y= f(x) = f(x0), f(x1), f(x2) , f(a + nh) i. e., f(xn) Let one of the value of f(x) is missing Say it f (i) To determine this missing value of f(x), assume...

Ngày tải lên: 04/07/2014, 15:20