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- Computer-based numerical & statistical techniques
- Computer Based Numerical Statistical Techniques
- Manish Goyal and N P Bali
- Books by Manish Goyal
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Computer-based numerical & statistical techniques
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ISBN hardcover with cd-rom : alk. Engineering mathematics --Data processing. G For additional information, please contact the Customer Service Dept. Requests for replacement of a defective CD-ROM must be accompanied by the original disc, your mailing address, telephone number, date of purchase and purchase price. We know that exact methods often fail in drawing plausible inferences from a given set of tabulated data or in finding roots of transcendental equations or in solving non-linear differential equations.
Even if analytical solutions are available, they are not amenable to direct numerical interpretation. The aim of numerical analysis is, therefore, to provide constructive methods for obtaining answers to such problems in a numerical form. With the advent of high speed computers and increasing demand for numerical solutions to various problems, numerical techniques have become indispensible tools in the hands of engineers and scientists.
Such equations are solved by numerical analysis. Methods of numerical analysis are used to approximate the problem satisfactorily so that an approximate solution, amenable to precise analysis, within a desired degree of accuracy is obtained. To attain a desired degree of accuracy, insight into the process and resulting error is essential. Three broad steps are incorporated in the process i Given data, called input information ii Algorithm iii The results obtained, called output information.
Input InformationThe Algorithm Output InformationComputers have changed, almost revolutionized, the field of numerical methods as a whole as well as many individual methods. That development is continuing. Much research is devoted to creating new methods, adapting existing methods to new computer generations, improving existing methods, and investigating stability and accuracy of methods. In large scale work, even small improvements bring large savings in time and storage space.
It accepts information or data from the outside world and processes it to produce new information. It also retrieves the stored information efficiency. Hence, "The computer is an electronic device capable of accepting information, applying prescribed processes to the information, and supplying the results of these processes.
A small circle with any number or letter in it is used as a connector symbol. It connects various parts of a flow-chart which are far apart or spread over pages. A rectangle with double vertical sides is used to denote a subprocess which is given elsewhere as indicated by connector symbol. When this box is encountered, the flow goes to the subroutine and it continues till a 'Return' statement is encountered.
Then it goes back to main flow-chart and flow resumes onward processing. The flow-chart can be translated into any computer language and can also be executed on the computer. A computer does not have the capability of reading and understanding instructions written in a natural language like English.
Thus, it is necessary to express the algorithm in a language understood by the computer. An algorithm coded in a computer language is called a program and the language used for coding is called a programming language. A single operation to be executed by the computer is called an instruction. The science that deals with the canons and criteria of validity in thought and demonstration, or the science of the formal principles of reasoning is called logic.
A series of instructions or one instruction in a program that isrepeated for a prescribed number of times, followed by a branch instruction that exits the program from the loop. A program designed to translate high level language source program into machine language object program is called a compiler. A machine language program that converts all instructions into the binary format. A program required on practically all systems that loads the user's program along with required system routines into the central processor for execution.
The set of grammatical rules defining the structure of a programming language is called syntax. An accumulation of unwanted, meaningless data after processing of any program is called Garbage. A drawback of these languages was that they were only suitable for specific purposes.
There was a need for a single computer language that could cater to the needs of different applications uniformly and efficiently. This led to the formation of an International Committee to develop such a language.
It did not become popular as it was too abstract and too general. These languages were again found to be either very big and exhaustive or less powerful. Languages can be classified into two categories: i High level languages Problem Oriented Languages. Hence 'C' is said to be a Middle level language as it stands between the above two categories. The following table shows the valid alphabets, digits, and special symbols allowed in 'C'; Alphabets: A, B, C, Digits: 0, 1,2, The alphabets, digits, and special symbol, when properly combined, form constants, variables, and keywords.
The three numbers are the input and the average is the output. Following are the tasks to be performed by the computer. Read the three numbers. Calculate the average. Output the average. The computer actually works as follows:n Reads the three numbers and stores them in three locations of memory.
The result is stored in a fourth location. When numbers are stored in various locations of memory, it becomes necessary to name each of the memory locations. The name of the memory location is called variable. Memory locations may contain integer, real, or character constants. Depending upon the data contained in the memory location, the variables are classified as integer, real, character, and string variables.
Secondary variables can be a Array variables b Pointer variables c Structure variables d Union variables e Enum variables. Their meanings are predefined and hence these words cannot be used as variable names. There are 32 key words in C language. Hierarchy of operations is given below: Priority Operators 1. Parentheses-All parentheses are evaluated first 2. Multiplication and division 3. Addition and Subtraction.
Each instruction in C program is written as a separate statement. However big a problem or program is, the following rules are applicable to all 'C' Statements: a Blank spaces may be inserted between two words to improve readability of the statement.
Any 'C' program is a combination of functions. Main is one such function. Empty parentheses after main is a must. The set of statements belonging to a function is enclosed within a pair of braces. Library functions are those which are available as a part of 'C' language C Compiler. These can be used by the programmers users directly to do a specific task. These sets are called header files in 'C'. The header file is denoted by the file extension h. The following table shows some popular library functions.
In the above C-program, the first line contains a reference to a header file. Library functions of stdio. If we want to use certain mathematical functions then the header file math.
The second line of the above program is a comment line. It can be anywhere in the program and any number of comment lines are allowed. This comment line improves the readability and helps the programmer to understand the program.
The function name main is written next. Function name is always followed by a set of parentheses. Arguments, if any, are placed within the parentheses. The opening brace and the closing brace indicate the beginning and end of the function.
Computer Based Numerical Statistical Techniques
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Manish Goyal and N P Bali
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 Report this Document. Carousel Previous Carousel Next.
Books by Manish Goyal
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