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The local convergence analysis of a parameter based iteration with Hölder continuous first derivative is studied for finding solutions of nonlinear equations in Banach spaces. It generalizes the local convergence analysis under Lipschitz continuous first derivative. The main contribution is to show the applicability to those problems for which Lipschitz condition fails without using higher order derivatives. An existence-uniqueness theorem along with the derivation of error bounds for the solution is established. Different numerical examples including nonlinear Hammerstein equation are solved. The radii of balls of convergence for them are obtained. A substantial improvement of these radii are found in comparison to some other existing methods under similar conditions for all examples considered.

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Sudoku is an interesting number placement puzzle with some simple rules. For some positive integer [Formula: see text], the puzzle involves an [Formula: see text] grid partitioned into [Formula: see text] distinct blocks each of size [Formula: see text] such that the integers [Formula: see text] through [Formula: see text] appear exactly once in each row, each column and each block of the grid. Often some static numbers known as givens are placed according to the difficulty rating in the puzzle and then the rule is to place the numbers from [Formula: see text] to [Formula: see text] in the partially filled grid such that the conditions of the puzzle are satisfied. The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size [Formula: see text]. It is based on the concepts of permutations derived from [Formula: see text] S-permutation matrices termed as S-permutations. There is a one-to-one correspondence between Sudoku squares and the set of those S-permutation matrices which are mutually disjoint to each other. The proposed algorithm uses the set of all S-permutations generated by some permutation generation algorithm as input and then enumerates all the subsets of cardinality [Formula: see text] of all S-permutations which are mutually disjoint to each other. The correctness of the algorithm is established. Its worst-case time complexity is O[Formula: see text], where [Formula: see text]. A mathematical formula involving the total number of the sets of [Formula: see text] mutually disjoint S-permutations is also derived. Experimentally, the proposed algorithm is verified for the Sudoku squares of size [Formula: see text]. It is observed that our algorithm is more systematic and better in terms of computational efficiency.

Abstract-Engineering and doctoral courses are considered to be golden professions for successful life. India is the largest Engineers' producing country, with changing technology, education system also has been changed from Gurukul to new modern technology based teaching system. Learning and knowledge are correlated terms, which go side by side and have imperative value and learning right knowledge from the best educational institute plays a vital role in one's life. IIT's, NIT's and Govt. institutes could not accommodate all the aspirants who have dreamed to be an engineer, certainly they are required to take admission in some private institutions. Due to numerous engineering institutes and universities this becomes a tedious job for both the parents and aspirants to select a perfect institution. Multi Attribute Decision Making (MADM) methods provide a ranking of the available alternatives thereby, decision of critical thinking become easier. The present paper examines the application of few MADM paradigms for selecting the most suitable academic institution, four state private universities of state Uttarakhand are considered as alternatives and evaluated and prioritized on seven major criterions.

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