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A textbook of Computer Based Numerical and Statiscal Techniques part 41

A textbook of Computer Based Numerical and Statiscal Techniques part 41. 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. | 386 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 2. Solve the following system of equations using Gauss-Elimination method a x - y z 1 b x 3y 6z 2 3x 2y 3z 6 x 4y 2z 7 2x 5y 4z 5 Ans. 2 3 6 3x y 4z 9 Ans. 2 1 c 5x y z u 4 z 7 y z u 12 x y 6z u 5 x y z u 6 Ans. 1 2 1 2 3. What do you understand by ill-conditioned equations Consider the following system of equations 100x 200y 100 200x 401y 100 Determine whether given system is ill-conditioned or not. 4. Solve the following system of equations by Jacobi s iterations method a 2x y 2z 17 b 5x 2y z 12 3x 20y z 18 x 4y 2z 15 2x 3y 20z 25 Ans. 1 -1 1 x 2y 5z 20 Ans. 1.08 1.95 3.16 5. Using Gauss-Seidel method solve the following system of equations a 10x y z 12 b 2x - y z 5 2x 10y z 13 2 3y - 2z 7 2x 2y 10z 14 Ans. 1 1 1 x 2y 3z 10 Ans. 3 2 1 c 20x y - 2z -17 3x 20y - z -18 2x - 3y 20z 25 Ans. 1 -1 1 CHAPTER Curve Fitting 9.1 INTRODUCTION In many branches of applied mathematics and engineering sciences we come across experiments and problems which involve two variables. For example it is known that the speed v of a ship varies with the horsepower p of an engine according to the formula p a bv3. Here a and b are the constants to be determined. For this purpose we take several sets of readings of speeds and the corresponding horsepowers. The problem is to find the best values for a and b using the observed values of v and p. Thus the general problem is to find a suitable relation or law that may exist between the variables x and y from a given set of observed values xir yi i 1 2 . n. Such a relation connecting x and y is known as empirical law. The process of finding the equation of the curve of best fit which may be most suitable for predicting the unknown values is known as curve fitting. Therefore curve fitting means an exact relationship between two variables by algebraic equations. There are following methods for fitting a curve I. Graphic method II. Method of group averages III. Method of moments IV. Principle .