Computer oriented numerical and statistical methods pdf
Computer Based Numerical and Statistical Techniques
Numerical analysis , area of mathematics and computer science that creates, analyzes, and implements algorithms for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of digital computers has led to an increasing use of realistic mathematical models in science and engineering, and numerical analysis of increasing sophistication is needed to solve these more detailed models of the world. The formal academic area of numerical analysis ranges from quite theoretical mathematical studies to computer science issues. With the increasing availability of computers, the new discipline of scientific computing, or computational science, emerged during the s and s. The discipline combines numerical analysis, symbolic mathematical computations, computer graphics , and other areas of computer science to make it easier to set up, solve, and interpret complicated mathematical models of the real world. Numerical analysis is concerned with all aspects of the numerical solution of a problem, from the theoretical development and understanding of numerical methods to their practical implementation as reliable and efficient computer programs.
Errors and their Computation, General error formula, Error in a series approximation Solution of Algebraic and Transcendental Equation: Bisection Method, Iteration method, Method of false position, NewtonRaphson method, Methods of finding complex roots, Mullers method, Rate of convergence of Iterative methods, Polynomial equations. Programming assignment based on above methods. Regression analysis: Linear and Non-linear regression, Multiple regression Unit-V Time series and forcasting: Moving averages, smoothening of curves, forecasting models and methods. Read Free For 30 Days. Computer Based Numerical and Statistical Techniques.
MCA Computer Oriented Numerical Method and Statistical Method. Faculty Code: (I) Which of the following method gives the comparatively faster.
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Computer Oriented Numerical & Statistical Methods
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Numerical analysis is the study of algorithms that use numerical approximation as opposed to symbolic manipulations for the problems of mathematical analysis as distinguished from discrete mathematics. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics predicting the motions of planets, stars and galaxies ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Before the advent of modern computers, numerical methods often depended on hand interpolation formulas applied to data from large printed tables. Since the mid 20th century, computers calculate the required functions instead, but many of the same formulas nevertheless continue to be used as part of the software algorithms. The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection YBC , gives a sexagesimal numerical approximation of the square root of 2 , the length of the diagonal in a unit square.
Course content Computer Arithmetic: Floating point representation of numbers, Arithmetic operations with normalized floating point numbers and their consequences, Error in number representation -Pitfalls in computing, Error propagation in evaluation. Successive approximation method, Newton raphson method for two variables, Discussion of convergence, Solving polynomial equations, Budan's theorem, Barirstow's method, Graeffe's root squaring method. Interpolation and Approximation: Polynomial interpolation, Truncation error in interpolation, Difference tables and calculus of differences, Cubic splines, Inverse interpolation, Linear regression and nonlinear regression using least square approximation, Approximation of function by Taylor Series and Chebyshev Polynomials. Numerical Differentiation And Integration: Differentiation dormulas based on polynomial fit, Pit-Falls in differentiation trapezoidal, Simpson's and gossip quadrature formulas. Computer Oriented Numerical Methods, R.