2,447 research outputs found
Subspace tracking in low-rank real-time systems
No full textErbay, Hasan/0000-0002-7555-541XThe truncated ULV decomposition (TULVD) provides good approximation to subspaces for the data matrix and can be modified quickly to reflect changes in the data. It also reveals the rank of the matrix. We develop an updating routine that is suitable for large scaled matrices of low rank. Numerical results presented that illustrate the accuracy of the algorithm. (c) 2005 Elsevier Inc. All rights reserved
An algorithm for rank estimation and subspace tracking
No full textErbay, Hasan/0000-0002-7555-541XThis article presents an URV-based matrix decomposition, the truncated URV decomposition, and an updating algorithm for it. The complexity of the updating is [image omitted] for an m-by- n matrix of rank r. The theoretical and numerical results presented shows that the decomposition can be a good alternative to the singular value decomposition
An alternative algorithm for a sliding window ULV decomposition
No full textErbay, Hasan/0000-0002-7555-541XThe ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be modified much faster than the SVD. When modifiying the ULVD, the accurate computation of the subspaces is required in certain time varying applications in signal processing. In this paper, we present an updating algorithm which is suitable for large scaled matrices of low rank and as effective as alternatives. The algorithm runs in O(n(2)) time
An efficient algorithm for rank and subspace tracking
No full textErbay, Hasan/0000-0002-7555-541XTraditionally, the singular value decomposition (SVD) has been used in rank and subspace tracking methods. However, the SVD is computationally costly, especially when the problem is recursive in nature and the size of the matrix is large. The truncated ULV decomposition (TULV) is an alternative to the SVD. It provides a good approximation to subspaces for the data matrix and can be modified quickly to reflect changes in the data. It also reveals the rank of the matrix. This paper presents a TULV updating algorithm. The algorithm is most efficient when the matrix is of low rank. Numerical results are presented that illustrate the accuracy of the algorithm. (c) 2006 Elsevier Ltd. All rights reserved
Kantorovich-type generalization of parametric Baskakov operators
No full textErbay, Hasan/0000-0002-7555-541X; ARAL, Ali/0000-0002-2024-8607In this manuscript, we define a Kantorovich generalization of the nonnegative parametric Baskakov operators. After that, the weighted uniform convergence of the generalized operators is proved. Also, we present Voronovskaja-type asymptotic approximation theorem then establish weighted approximation properties for parametric Kantorovich operator. Numerical results show that depending on the value of the parameter, we obtain a better approximation
Comparison of Two-Parameter Bernstein Operator and Bernstein-Durrmeyer Variants
No full textErbay, Hasan/0000-0002-7555-541XThe quantum calculus and the post-quantum calculus have recently gained broad popularity in computational science and engineering due to their applications to diverse areas such as solution of differential equations, approximation theory and computer-aided geometric design. Herein, we consider two parameters but two different modified Bernstein-Durrmeyer operators along with two-parameter Bernstein operator. We obtain estimates to the differences between the Bernstein operator and each modified Bernstein-Durrmeyer operator using classical modulus of continuity. In addition, similar estimates are obtained for Chebyshev functional of these operators. Main purpose of using two-parameter operators is to allow us more flexible approximations compared to their classical versions, namely depending on values of parameters, the approximation can be speeded up. Numerical results presented approves the theoretical results
Modifiable low-rank approximation to a matrix
No full textErbay, Hasan/0000-0002-7555-541XA truncated ULV decomposition (TULVD) of an m x n matrix X of rank k is a decomposition of the form X=ULVT + E, where U and V are left orthogonal matrices, L is a k x k non-singular lower triangular matrix and E is an error matrix. Only U,V, L and parallel to E parallel to(F) are stored, but E is not stored. We propose algorithms for updating and downdating the TULVD. To construct these modification algorithms, we also use a refinement algorithm based upon that in (SIAM J. Matrix Anal. Appl. 2005; 27(1):198-211) that reduces parallel to E parallel to(F), detects rank degeneracy, corrects it, and sharpens the approximation. Copyright (C) 2009 John Wiley & Sons, Ltd
V. Uluslararası Farklı Boyutlarıyla Sağlık Konferansı / Tam Metinler Kitabı
No full textThis volume, edited by Assoc. Prof. Dr Hasan Erbay and Prof. Dr. Özge Uysal Şahin compiled the full-text proceedings from the V. International Conference on Different Aspects of Health (ICDAH 2024). The book offers an international and multidisciplinary perspective on current challenges in the health sector. It features research on a wide variety of contemporary topics, including One Health, the effects of climate change on women's Health, pandemic management , disaster nursing, health services access for the elderly, and childhood epilepsy. This collection serves as a valuable resource for health professionals, academics, and policymakers.Doç. Dr. Hasan Erbay ve Prof. Dr. Özge Uysal Şahin'in editörlüğünü üstlendiği bu eser, V. Uluslararası Farklı Boyutlarıyla Sağlık Konferansı (ICDAH 2024) kapsamında sunulan tam metin bildirileri bir araya getirmektedir. Kitap, sağlık alanındaki güncel zorluklara uluslararası ve multidisipliner bir bakış açısı sunmaktadır. İçeriğinde Tek Sağlık, iklim değişikliğinin kadın sağlığı üzerindeki etkileri , pandemi yönetimi , afet hemşireliği , yaşlı bireylerin sağlık hizmetlerine erişimi ve çocukluk çağı epilepsisi gibi çok çeşitli ve güncel konuları ele alan araştırmalar bulunmaktadır. Bu derleme, sağlık profesyonelleri, akademisyenler ve politika yapıcılar için değerli bir kaynak niteliğindedir
Weibull distribution and its applications
No full textÖZETWE BULL DAĞILIMI VE UYGULAMALARIEL TOK, ÖzkanKırıkkale ÜniversitesiFen Bilimleri EnstitüsüMatematik Anabilim Dalı, Yüksek Lisans TeziDanışman : Doç. Dr. Hasan ERBAYEK M 2006, 59 SAYFAWeibull dağılımı bir çok alanda yaygın olarak kullanılmaktadır. Weibulldağılımı kuvvet karakteristiği eğrisinin tüm bölgelerini temsil edebilmektedir. Buözelliği, güvenilirlik çalışmalarında Weibull dağılımını diğer dağılımlara göre dahakullanışlı kılmaktadır.Bu tezde, Weibull dağılımının incelenmesi ve uygulama alanlarınıngösterilmesini amaç edinilmiştir. Bilimsel literatürün taranması, bu çalışmanın ilkadımını teşkil etmektedir. Ardından verilerin Weibull dağılımına uyumluluğunu testiçin kullanılan yöntemler, parametre tahmin yöntemleri, parametre ve yüzdelikleriçin güven aralıkları üreten yöntemler incelenmiştir. Son olarak da Weibull dağılımındağılımının uygulanması ele alınmıştır.Anahtar Kelimeler: Weibull Dağılımı, Maksimum Benzerlik Yöntemi, En-KüçükKareler Yöntemleri ve Weibull Dağılımı uygulamalarABSTRACTWEIBULL DISTRIBUTION AND ITS APPLICATIONSÖzkan EL TOKKırıkkale UniversityGraduate School Of Natural and Applied SciencesDepartment of Mathmetic, M. Sc. ThesisSupervisor : Assoc. Hasan ERBAYOCTOBER 2006, 59 PAGESWeibull distribution has been used in a lot of field as common. Weibulldistribution is able to represent all regions of the bathtub curve. This feature makesWeibull distribution more useful than other distributions in reliability studies.Our goal in this thesis is to analyze Weibull distribution and show some of itsapplications.The first step is the survey of the related scientific literature. Then,goodness-of-fit tests for Weibull distribution, parameter estimation methods andconfidence interval methods for parameters and percentiles are analyzed.Finally, it is checked that Reliability analysis, one of applicational fields ofWeibull distribution.Key Words: Maximum Likelihood Method, Least-squares methods and WeibullDistribution Applications
Improved Gram–Schmidt Type Downdating Methods
No full textErbay, Hasan/0000-0002-7555-541XThe problem of deleting a row from a Q-R factorization (called downdating) using Gram-Schmidt orthogonalization is intimately connected to using classical iterative methods to solve a least squares problem with the orthogonal factor as the coefficient matrix. Past approaches to downdating have focused upon accurate computation of the residual of that least squares problem, then finding a unit vector in the direction of the residual that becomes a new column for the orthogonal factor. It is also important to compute the solution vector of the related least squares problem accurately, as that vector must be used in the downdating process to maintain good backward error in the new factorization. Using this observation, new algorithms are proposed. One of the new algorithms proposed is a modification of one due to Yoo and Park [BIT, 36:161-181, 1996]. That algorithm is shown to be a Gram-Schmidt procedure. Also presented are new results that bound the loss of orthogonality after downdating. An error analysis shows that the proposed algorithms' behavior in floating point arithmetic is close to their behavior in exact arithmetic. Experiments show that the changes proposed in this paper can have a dramatic impact upon the accuracy of the downdated Q-R decomposition
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