This nal project discusses the generalization of Gauss-Seidel iteration method, by forming splitting like the Gauss Seidel method, to solve the system of absolute value equations. Before proving the convergence of the method, rst an analysis is carried out on how to obtain solutions from the application of the generalization of the Gauss-Seidel method. The convergence of the discussed me…
This nal project discusses the assignment problems. This type of assignment problem is completed by using a least cost technique. The result of this method is to minimize or maximimize the objective function in balanced or unbalanced cases, which aims to the lowest cost assignment. Illustrative examples with a least cost assignment method are given as an alternative to the Hungarian metho…
This nal project discusses the solution of assignment problems with a cost matrix in intervals. The assignment problem is completed by modifying the cost matrix becomes the cost matrix in intervals and solved using the Hungarian method. The purpose of this method is to minimize the cost of the assignment so that the optimal cost are obtained. An illustrative examples is given to show the …
This project discusses a quadratic approximation method of the Riemann-Liouville fractional integral and Caputo’s fractional derivative. A quadratic polynomian is used to approach function that appear in the definitions of Riemann-Liouville fractional integral and Caputo fractional derivative. Using this polynomial, a quadratic approximation formula of Riemann-Liouville fractional integr…
A partition of a positive integer is the representation of the positive integer its self or sums of other positive integers, while the partition function is the number of partitions. This nal project disscusses a method to compute the values of the partition function using Ewell's method and Merca's method. This is a review of some parts of Merca's paper [Journal of Number Theory, 164 (201…
This final project discusses a new generalization of Fibonacci sequence called the Fibonacci-like sequence. Furthermore it discusses the relation between Fibonacci-like sequence and k-Lucas sequence by introducing special matrix. By using the matrix, Cassini’s identity for Fibonacci-like sequence, and some relations between Fibonacci-like sequence and k-Lucas sequence are obtained. Then …
This final project discusses application of determinant matrix whose elements are triangular fuzzy number in the form of parameters. At the beginning it is shown that the properties that apply to real number also apply to triangular fuzzy number. Furthermore, it is shown that some matrix properties for real number also apply to fuzzy matrix. Development of triangular fuzzy number concept b…
This final project discusses the proof for q-analogue of the Riordan representation of the q-Pascal matrices and q-analogue of the Riordan representation for its invers q-Pascal matrix. This project is completed by using binary operations ∗q for q-Pascal matrices and binary operations ∗1=q for invers q-Pascal matrix. This final project is a review of some parts of article Tu˘glu et al.…