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Iterative Methods for Solving Systems of Equations

Thesis Info

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Author

Iqbal, Javed

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1632

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726563045

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Iterative Methods for Solving Systems of Equations It is well known that a wide class of problems, which arises in pure and applied sciences can be studied in the unified frame work of the system of absolute value equations of the type Ax − x = b, A ∈ Rn×n , b ∈ R n . Here x is the vector in R n with absolute values of components of x. In this thesis, several iterative methods including the minimization technique, residual method and homotopy perturbation method are suggested and analyzed. Convergence analysis of these new iterative methods is considered under suitable conditions. Several special cases are discussed. Numerical examples are given to illustrate the implementation and efficiency of these methods. Comparison with other methods shows that these new methods perform better. A new class of complementarity problems, known as absolute complementarity problem is introduced and investigated. Existence of a unique solution of the absolute complementarity problem is proved. A generalized AOR method is proposed. The convergence of GAOR method is studied. It is shown that the absolute complementarity problem includes system of absolute value equations and related optimizations as special cases
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ڈاکٹر حامد اﷲ ندوی

ڈاکٹر حامد اﷲ ندوی
ڈاکٹر حامد اﷲ ندوی کے انتقال کی افسوس ناک خبر تاخیر سے ملی، انہوں نے ۱۹؍ اکتوبر ۹۹؁ء کو سنگاپور میں داعی اجل کو لبیک کہا، ان کا وطن تامل ناڈو کی مشہور ریاست آرکوٹ (نارتھ) کا ایک قصبہ چروتاپور تھا۔ یہیں وہ ۱۹۲۵؁ء میں پیدا ہوئے اور ابتدائی تعلیم حاصل کرنے کے بعد دارالعلوم ندوۃ العلماء میں داخلہ لیا، ندوہ سے فراغت کے بعد پونے یونیورسٹی سے فارسی اور اردو میں ایم۔اے کیا۔
درس و تدریس کا آغاز بمبئی کے مشہور تعلیمی ادارے انجمن اسلام سے ہوا، اس کے ریسرچ سنٹر سے بھی وابستہ رہے اور عرصہ تک مہاتما گاندھی میموریل سنٹر کی ہندوستانی پرچار سبھا سے منسلک رہے، جس کے ڈائریکٹر پروفیسر عبدالستار دلوی تھے۔ اسی زمانے میں ہمارے سابق رفیق مولانا عبدالرحمن پرواز اصلاحی کا تعلق بھی اس سینٹر سے تھا، انہی کے ہم راہ راقم نے پہلی بار ان دونوں حضرات سے ملاقات کا شرف حاصل کیا، دونوں دارالمصنفین کے بڑے قدرداں اور خیر خواہ تھے اس لیے مجھ سے بڑے اخلاص، محبت اور گرم جوشی سے ملے اور توقع سے زیادہ میری پذیرائی کی۔
آخر میں ڈاکٹر حامد اﷲ ندوی کا تعلق بمبئی یونیورسٹی کے شعبہ عربی سے ہوگیا، اس سے وظیفہ یاب ہونے کے بعد بمبئی کی ہنگامہ خیز زندگی سے الگ رہ کر وہ خاموشی سے علمی، ادبی اور تحقیقی کاموں میں مشغول رہتے تھے جس سے ان کو بڑا شغف تھا۔ تحریر و تصنیف کا بھی اچھا ذوق اور خاص سلیقہ تھا جس کا ثبوت ان کی تصنیفات ہیں جو تلاش، تحقیق اور محنت و جستجو سے لکھی گئی ہیں۔
ان کی کتاب ’’لکھنؤ کی لسانی خدمات‘‘ شایع ہوئی تو علمی حلقوں میں اس کی بڑی پذیرائی ہوئی، دوسری کتابیں ’’اردو کی چند نایاب مثنویاں‘‘ اردو کے چند نامور ادیب اور شاعر ’’ہندوستان اور مشرق وسطیٰ...

Economic Facilities for Non-Muslims in a Muslim Country in the Light of Quran and Sunnah

The question of economic facilities for non-Muslims in a Muslim country has been one of the most important questions in the Muslim and non-Muslim world. It has been highlighted by some economists and jurists about their economic facilities. This paper is intended to discuss the economic facilities for non-Muslims in a Muslim country in the light of Quran and Sunnah and the Islamic history. It is the topmost responsibility of the Islamic state/Muslim country to fulfill the basic needs of human life and to encourage voluntary services for the welfare of the poor, to promote equal opportunities in a Muslim country, to enforce social and economic justice in Islam, to provide social security and basic economic facilities, and to give a fair share of economic rights to all citizens. The Government should also provide employment (services), Jizyah and to impose tax on non-Muslims. It will be shown that in Muslim countries, all non-Muslims have equal economic opportunities and rights as other Islamic citizens and also the same status in terms of Islamic economy. This paper may also throw some light on the Islamic Philosophy of economy in the contemporary Muslim world and explore the constituents and effects of an Islamic/Muslim anti-economy policy. This paper will conclude by providing some suggestions on ways of solving contemporary non–Muslim economic problems in Muslim countries nowadays.

مکتوبات مولوی محمد حسین آزاد کا تحقیقی اور تنقیدی جائزہ

Letters written by famous writers have contributed a great deal in the development of Urdu language and literature. Today, this significantly important type of prose writing is on decline, due to advancement in the field of communication. Hence, communication through letters is being substituted with SMS, MMS, templates and e-mails etc., which are not being preserved for subsequent analysis. So far, letters of only few famous writers have been researched & critically analyzed, for their literary importance. It is in this back drop that the letters of Muhammad Hussain Azad, who is regarded as one of the five important learned persons of Urdu prose writing, have been selected for research and critical analysis. My endeavor was to highlight the ignored aspects of Azad's prose and an effort in this direction has been made through literary analysis of various letters. For ease of understanding, I have segregated my research into six chapters; each one elucidating distinctly, important aspects of my research. The first chapter is about tradition of Urdu letter writing from its infancy till Sir Syed Ahmed Khan. The 2nd chapter discusses the letter writing style of Azad's counter parts, whereas 3rd chapter presents Azad's biography, literary services and style of expression in prose. Fourth chapter focuses on the research of Azad's letters whereas 5th chapter offers critical analysis of his letters and style of letter writing. The chapter also focuses on Azad's biography derived from his letters & Azad's style of letter writing in relation to his overall style of prose writing. Last chapter briefly describes addresses.