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Showing posts from February, 2014

Finding the Area of a polygon

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Area of a polygon Abstract — This work discusses finding out the are of a given polygon with n number of edges or sides. The time complexity and scalability of the algorithm are analyzed. The results indicate that the algorithm is scalable and efficient. Keywords: polygon, triangles, polygon. I.       Introduction Area of a given polygon with n number of edges can be found by different methods like finding the centroid of a given polygon then apply area formula to get the area of that polygon. Using the divide and conquer technique to find the area of a given polygon, this technique is used when the given problem is larger or more complex then divide the problem until we get smaller subproblems than find solutions for that smaller subproblems then combine the results of smaller subproblems. Now we obtain the result for a complex problem. To find the area for a triangle (a simple polygon) we know the formula to find the area. Area =  ½...

Restructuring iterative algorithms under sparse conditions

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Restructuring iterative algorithms under sparse conditions Abstract — This paper discusses finding out the given sparse matrix is diagonally dominant or not, by solving a set of simultaneous equations using iterative algorithms like Gauss-Seidel and Jacobi method. The time complexity and scalability of the algorithm is analyzed. The results indicate that the algorithm is scalable and efficient. I.       Introduction Iterative schemes require time to achieve sufficient accuracy and are reserved for large systems of equations where there are a majority of zero elements in the matrix. Often times the algorithms are Taylor-made to take advantage of the special structure such as band matrices. Practical uses include applications in circuit analysis, boundary value problems, and partial differential equations.         Iteration is a popular technique finding the roots of equations.  Generalization of fixed-point i...