Preamble: This is M.Tech.(IT)-V Semester's core subject of Computer Science.It is termed by various names like:
- Numerical Analysis and Design (NAD)
- Design and Analysis of Numerical Algorithms ( D&A of NM )
- Design of Numerical Algorithms ( DNA )
- Computer Oriented Numerical Methods (CONM )
- Computer Oriented Numerical and Statistical Methods ( CONSM )
- Numerical Analysis ( NA )
These subjects are taught in various courses with different perspective. In this class the subject will be discussed with the perspective of Development and Analysis of algorithms for Numerical Problems.
The Theoretical base/Concept will be discussed in detail with the approach of developing algorithms.
and the result of algorithm will be analysed by various alternatives.A comparative study of these algorithms will be attempted with the focus of efficient algorithms.
The Sequence in which each method will be discussed is:
- Derivation,Geometrical Interpretations
- Development of Algorithms/Flowchart
- Development of program/Coding
- Numerical problems
- Efficiency comparisons with peer algorithms
Numeric Information Representation :
- Integer Representations
- Unsigned integer representations
- One's Complement Method
- Two's Complement Method
- Real Number Representations
- Fixed Point Notations
- Floating Point Representations
- Arithmetic using floating point representations
- Consequences of floating point representations
- Concept of Zeros
- Errors in handling numerical quantities and Measures and types of errors.
- Problems and Solutions
UNIT-2 Roots of Polynomials: Concept of roots, Formula approach v/s Iterative approach, Iterative Methods:
- LAB Assignment
- Statistical Computation Algorithms
- Study and develop Algorithms for:
- Frequency chart,Scatter diagrams,correlations
- Curve fitting by method of least squares
- fitting of straight lines, polynomials, exponential curves etc,
- Data fitting with Cubic splines,
- Regression Analysis, Linear and Non linear Regression, Multiple regression
- Rajaraman V, “Computer Oriented Numerical Methods”, Pearson Education
- IGNOU Study Materials
- Gerald & Whealey, “Applied Numerical Analyses”, AW
- Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age Int.
- Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi
- T Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods,TMH
- Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH
- Francis Scheld, ” Numerical Analysis”, TMH
- Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.
- Gupta C.B., Vijay Gupta, “Introduction to Statistical Methods”, Vikas Publishing.
- Goyal, M, “Computer Based Numerical and Statistical Techniques”, Firewall Media, New Delhi.
- Use Python/C to see and demonstrate your computations results graphically
- Use MATLAB, NUMPy, SciLab for solving all the problems of Unit1,2,3,4,5
Teaching Aid-(Future Action-2014)
- Shifting whole course on Moodle
- Video Lectures on DAVV-Tube
Root Finding techniques
System of equation
- Forward difference interpolation
- Backward difference interpolation
- Divided difference interpolation
- Lagrangee's interpolation
- Bisection Method/Bolzano's Method/Midpoint subdivision Method
- Method of false position/Regula Falsi Method
- Secant Method
- Newton Raphson Method
- Convergence Order Theorem
- Order of Convergence of Secant Method
- Order of Convergence of Newton Raphson Method
- Comparison among various iterative methods
- Function with discrete arguments, Basics of Finite difference calculus.
- Forward difference operator, Forward difference table,
- Algorithm/program/flowchart for construction of forward difference tables.
- Backward difference operator,Backward difference table, algorithm/program/flowchart for construction of Backward difference tables.
- Divided difference operator,Divided difference table, algorithm/program/flowchart for construction of Divided difference tables.
- Shift Operator, Central difference operator, Averaging operator
- Relationship among various operators.
- Concepts of interpolation,Purpose of interpolation,
- Newton Gegory Forward interpolation formula, Newton Gregory Backward interpolation formula, Newton's divided difference interpolation formula,
- Lagrangee's interpolation formula,Inverse interpolation.Numerical problems and algorithms/ Programs.
- Inverse Interpolation
UNIT-5: Numerical Differentiation and Integration
- Newton Cote's formula,General Quadrature Formula,
- Derivation of Trapezoidal rule, Simpson's rule (1/3 and 3/8), Weedle's Rule,(Algorithms, programs, numerical)
- Numerical Differentiation.
- Solution of ordinary differential equations
- Solution of differential Equations using:
- Picard’s Method, Euler’s Method, Taylor’s Method,Runge - Kutta Methods, Predictor Corrector Methods