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Improving Halley and Householder Methods Using Decomposition Techniques

Thesis Info

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External Link

Author

Saira Sultan

Institute

Virtual University of Pakistan

Institute Type

Public

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Software Engineering

Language

English

Link

http://vspace.vu.edu.pk/detail.aspx?id=355

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676721031835

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In this thesis, two new methods for solution of nonlinear system of equations f(x) = 0 using two decomposition techniques are established, first is Adomian decomposition technique and second is Varsha decomposition technique. We expand f(x) to second order then apply both of these techniques one by one. The convergence order of both these algorithms is three and efficiency index is p 1/d =1.442. The main benefit of this scheme is that we get root of function even after one or two iterations, obviously has minimum computational complexity as compare to previous systems. Both methods almost give the same results and convergence orders. In practice, for large scale problems, many iterative methods can be derived by using two decomposition techniques with some modifications in Newton Raphson method. The order of convergence of new iteration formulas can be derived analytically and with the help of Maple. Some examples are given to illustrate the performance and precision of new algorithms. These algorithms can be assumed as generalization of old methods for solving nonlinear equations.
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مولانا عبداﷲ غازی پوری

مولانا حافظ عبداﷲ صاحب غازیپورؔی

            جناب مولانا عبداﷲ صاحب غازی پوری کا واقعہ وفات علماء کے طبقہ میں خاص حیثیت سے اثر انگیز ہے، مولانائے مرحوم نے گو طبعی عمر پائی لیکن اس خیال سے کہ وہ اس عہد میں اگلی صحبتوں کے تنہا یادگار تھے۔ ہم ان کے لئے اس سے دراز عمر کے متوقع تھے، مولانا اتباعِ سنت، طہارت تقویٰ، زہد و ورع، تبحرعلم، وسعتِ نظر اور کتاب و سنت کی تفسیر و تعبیر میں یگانۂ عہد تھے، اپنی عمر کا بڑا حصہ انہوں نے علم دینیہ خصوصاً کتاب مجید اور حدیث شریف کے درس و تدریس میں گزارا اور سینکڑوں طلبہ انکے فیض تربیت سے علماء بن کر نکلے، ابتداً چشمۂ رحمت غازیپور میں، پھر مدرسہ احدیہ آرہ میں اپنا مسندِ درس بچھایا، آخر عمر میں دلّی کے دارالحدیث میں قیام فرمایا، لیکن خانگی حوادث کے باعث پریشان حال رہے، اب افسوس کہ یہ شمع نورو ہدایت ۲۱؍ صفر ۱۳۳۷؁ھ مطابق ۲۶؍ نومبر، ۱۹۱۸؁ء کو ہمیشہ کے لئے بجھ گئی۔ رحمہ اﷲ تعالیٰ۔

            مجھے لکھنؤ میں مولانا عبدالحئی صاحب ناظم ندوہ کی قیام گاہ پر مولانا سے ملاقات کی سعادت ایک دو دفعہ حاصل ہوئی دُبلے، پتلے، نخیف، داڑھی کے بال خفیف، سادی وضع، صورت سے متواضع اور حلیم معلوم ہوتے تھے۔

            مرحوم کا اصلی وطن گومؤ ضلع اعظم گڑھ تھا، مگر قیام بیشتر غازی پور میں رہا، اس لئے غازیپوری کے نام سے شہرت پائی، ابتدائی تعلیم چشمۂ رحمت غازی پور میں ہوئی، یہاں مولوی رحمت اﷲ صاحب غازی پوری، اور مولوی فاروق صاحب چریا کوٹی سے پڑھا، پھر جونپور جاکر مدرسۂ امام بخش میں مفتی محمد یوسف صاحب فرنگی محلی سے درسیات پڑھیں اور آخر میں حدیث کی کتابیں مولانا سید نذیر حسین صاحب دہلوی سے پڑھیں اور...

Ambulatory Hysteroscopy in Abnormal Uterine Bleeding: A Tertiary Care Hospital Perspective

Background: To avoid delays in outpatient facilities for managing benign gynecological conditions like abnormal uterine bleeding (AUB), there is a need to evaluate the usage of unconventional methods like outpatient hysteroscopy. Objectives: To evaluate the usage of outpatient diagnostic hysteroscopy in women with abnormal uterine bleeding. Methods: An observational study was conducted at the Obstetrics and Gynecology Department of Combined Military Hospital, Kharian. The study included 56 women having AUB with or without a history of failed medical treatment. The study participants underwent outpatient diagnostic hysteroscopy. Diagnostic hysteroscopy was done under the local para-cervical block in the Outpatient department. Procedure indications, outcome and biopsy findings were recorded on predesigned proformas. Results: Median age of the study participants was 44 years. The most common indications for diagnostic hysteroscopy were postmenopausal bleeding (34%) and heavy menstrual bleeding (28%). Hysteroscopy outcomes included endometrial biopsy (34%), discharge with no biopsy (25%), further test and evaluations required (21%), and admission due to failed outpatient procedures (20%). Sixty-two percent of the study participants had normal biopsy findings while other biopsy findings included polyps (20%), fibroids (14%) and endometrial hyperplasia (4%). Nine percent had unsuccessful hysteroscopy due to patient refusal to proceed. Conclusion: Outpatient hysteroscopy can be helpful in the early and rapid diagnosis of women with abnormal uterine bleeding.  

Factors Associated With Development of Retinopathy of Prematurity in Three Private Tertiary Hospitals in Kenya

Introduction: Retinopathy of prematurity (ROP) is a condition that affects mainly premature infants. It’s characterized by abnormal retinal vascular growth which in its most severe form can result in blindness due to retinal detachment, and in less severe untreated forms, can result in marked visual impairment. Retinopathy of prematurity is one of the preventable causes of blindness. Research Question: What are the factors associated with development of retinopathy of prematurity in screened preterm infants in three private tertiary hospitals in Kenya? Study Objectives: This study aimed to identify factors associated with development of retinopathy of prematurity in screened preterm infants in three private tertiary hospitals in Kenya. It also aimed to determine the proportion of preterm infants with retinopathy of prematurity in the screened preterm infants within these three hospitals. Study Methods: This was an unmatched case control study, targeting records of preterm infants born between January 2010 to December 2017, in three private tertiary hospitals in Kenya. Data extracted was on gestational age at birth, birth weight, gender, duration of supplemental oxygen, occurrence of sepsis, intra ventricular hemorrhage and blood transfusion. The outcome assessed was a binary variable, defined as retinopathy of prematurity status, Positive or Negative. Results: A total of 228 patient records were included in the study. Overall proportion of ROP positive cases was 43.3% (95% CI: 36.9%-50.1%). Approximately half, (50.8%) of the babies who were put on oxygen supplementation for more than one week were ROP positive, however the proportions were similar for babies with and those without sepsis at 58.0% and 55.0% respectively. The proportion of preterm infants with ROP was lower in babies who were transfused compared to those who were not transfused (48.6% vs 63.6%). Gestational age (p-value=0.002), duration of oxygen therapy (p-value=0.012), and blood transfusion (p-value=0.022) were independently associated with ROP infection. Conclusion and Recommendations: The proportion of preterm infants who screened ROP positive in this study was 43.4% which was used as a proxy for prevalence of this condition in screened preterm infants in these three facilities. This serves as an indicator of the burden of this condition on preterm infants. Associated factors from this study were gestational age at birth, duration of supplemental oxygen and blood transfusion. Early weaning off from supplemental oxygen and judicious transfusions could possibly make an impact in reducing the prevalence of this condition. We recommend that there should be a national policy on screening of