Functions of structured matrices
Başlık çevirisi mevcut değil.
- Tez No: 403339
- Danışmanlar: Prof. NICHOLAS HIGHAM, Prof. FRANCOISE TISSEU
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2017
- Dil: İngilizce
- Üniversite: The University of Manchester
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 153
Özet
Özet yok.
Özet (Çeviri)
The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The rst part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matrices as an alternative to the algorithms using the Schur decomposition to compute the logarithm of symplectic matrices. There are two main calculations in the inverse scaling and squaring method: taking a square root and evaluating the Pade approximants. Numerical experiments suggest that using the Schur-like form with the structure preserving iterations for the square root helps us to exploit the Hamiltonian structure of the logarithm of symplectic matrices. Some type of matrices are nearly structured. We discuss the conditions for using the nearest structured matrix to the nearly structured one by analysing the forward error bounds. Since the structure preserving algorithms for computing the functions of matrices provide advantages in terms of accuracy and data storage we suggest to compute the function of the nearest structured matrix. The analysis is applied to the nearly unitary, nearly Hermitian and nearly positive semi-de nite matrices for the matrix logarithm, square root, exponential, cosine and sine functions. It is signi cant to investigate the e ect of the structured perturbations in the sensitivity analysis of matrix functions. We study the structured condition number of matrix functions de ned between smooth square matrix manifolds. We develop algorithms computing and estimating the structured condition number. We also present the lower and upper bounds on the structured condition number, which are cheaper to compute than the \exact" structured condition number. We observe that the lower bounds give a good estimation for the structured condition numbers. Comparing the structured and unstructured condition number reveals that they can di er by several orders of magnitude. Having discussed how to compute the structured condition number of matrix functions de ned between smooth square matrix manifolds we apply the theory of structured condition numbers to the structured matrix factorizations. We measure the sensitivity of matrix factors to the structured perturbations for the structured polar decomposition, structured sign factorization and the generalized polar decomposition. Finally, we consider the unstructured perturbation analysis for the canonical generalized polar decomposition by using three di erent methods. Apart from theoretical aspect of the perturbation analysis, perturbation bounds obtained from these methods are compared numerically and our ndings show an improvement on the sharpness of the perturbation bounds in the literature.
Benzer Tezler
- Depo tasarım sorunu analizi: Bir analitik ağ süreci uygulaması
Analysis of warehouse design problem: An analytic network process application
FATİH ÖZDEMİR
Yüksek Lisans
Türkçe
2004
Endüstri ve Endüstri Mühendisliğiİstanbul Teknik ÜniversitesiEndüstri Mühendisliği Ana Bilim Dalı
YRD. DOÇ. DR. İLKER TOPÇU
- Polivinil alkol/kitosan kriyojellerin biyomimetik hidroksiapatit ile kaplanmış kompozitlerinin üretilmesi ve karakterizasyonu
Production and characterization of biomimetic hydroxyapatite coated polyvinyl alcohol/chitosan composites
GÜLŞAH GÜL
Yüksek Lisans
Türkçe
2018
Kimya MühendisliğiMersin ÜniversitesiKimya Mühendisliği Ana Bilim Dalı
DOÇ. DR. NİMET KARAGÜLLE
- Lojik devre tasarımı algoritmaları
Başlık çevirisi yok
ORHAN UÇAR
Yüksek Lisans
Türkçe
1996
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiPROF.DR. AHMET DERVİŞOĞLU
- A^(1/2) için Steffensen yöntemi
Steffensen method for A^(1/2)
TUĞÇE ÜNAL
Yüksek Lisans
Türkçe
2024
MatematikBursa Teknik ÜniversitesiMatematik Ana Bilim Dalı
DR. ÖĞR. ÜYESİ BAHAR ALVEROĞLU
- Prioritizing the strategic objectives by integrating the AHP decision model with the strategy map – an applied study
AHP karar modelinin strateji haritası ile entegre edilmesi ile stratejik hedeflerin önceliklendirilmesi – uygulamalı çalışma
SÜMEYYE AKKOÇ
Yüksek Lisans
İngilizce
2024
Endüstri ve Endüstri Mühendisliğiİstanbul Teknik ÜniversitesiEndüstri Mühendisliği Ana Bilim Dalı
PROF. DR. YUSUF İLKER TOPCU