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Iterative methods for Moore-Penrose inverse

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dc.contributor.advisor Zein, Ali
dc.contributor.author Abu-Iram, Zainab
dc.date.accessioned 2019-01-28T11:33:15Z
dc.date.accessioned 2022-05-11T11:52:15Z
dc.date.available 2019-01-28T11:33:15Z
dc.date.available 2022-05-11T11:52:15Z
dc.date.issued 12/1/2018
dc.identifier.uri http://test.ppu.edu/handle/123456789/1299
dc.description no of pages 72 , 1/2018 mathematics, 31013 , master
dc.description.abstract The Moore-Penrose inverse is one of the most important generalized inverses for arbitrary singular square or rectangular matrix. It finds many applications in engineering and applied sciences. The direct methods to find such inverse is expensive, especially for large matrices. Therefore, various numerical methods have been developed to compute the Moore-Penrose inverse. This thesis is mainly concerned with the development of iterative methods to compute the Moore-Penrose inverse. Besides our new results the thesis contains several recent known iterative methods. The convergence properties of these methods are presented. And, several numerical examples are given. Our own results involve new family of second-order iterative algorithms for computing the Moore-Penrose inverse. The construction of this algorithm is based on the usage of Penrose equations with approximations for p-th root for a product of the matrix with its inverse approximations. Convergence properties are considered. Numerical results are also presented and a comparison with Newton’s method is made. It is observed that the new methods require less number of iterations than that of Newton’s method. In addition, numerical experiments show that these methods are more effective than Newton’s method when the number of columns increases than the number of rows. In addition, we establish a new iterative scheme by using a square of the product of the matrix with its inverse approximations. By convergence analysis, we show that this scheme is also a second order. Several numerical tests are made. It is observed that the above family is more effective than this method. en_US
dc.language.iso en en_US
dc.publisher جامعة بوليتكنك فلسطين - رياضيات en_US
dc.subject Iterative methods en_US
dc.subject Moore-Penrose inverse en_US
dc.title Iterative methods for Moore-Penrose inverse en_US
dc.type Other en_US

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