In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the image-based data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory. Copyright c (cid:13) 2022 Shahid Beheshti University.
{"title":"Tensor LU and QR decompositions and their randomized algorithms","authors":"Yuefeng Zhu, Yimin Wei","doi":"10.52547/cmcma.1.1.1","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.1","url":null,"abstract":"In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the image-based data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory. Copyright c (cid:13) 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127162799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Samundra Regmi, I. Argyros, S. George, Christopher I. Argyros
A ball convergence comparison is developed between three Banach space valued schemes of fourth convergence order to solve nonlinear models under ω − continuity conditions on the derivative. Copyright c (cid:13) 2022 Shahid Beheshti University.
{"title":"Ball comparison between three fourth convergence order schemes for nonlinear equations","authors":"Samundra Regmi, I. Argyros, S. George, Christopher I. Argyros","doi":"10.52547/cmcma.1.1.56","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.56","url":null,"abstract":"A ball convergence comparison is developed between three Banach space valued schemes of fourth convergence order to solve nonlinear models under ω − continuity conditions on the derivative. Copyright c (cid:13) 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121695478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a model based on data envelopment analysis is used for comparing different image segmentation methods and also for the purpose of finding the best parameter among certain values for a method. The criteria for choosing inputs and outputs are explained and in the end, some examples are presented to demonstrate how this model works. Copyright c (cid:13) 2022 Shahid Beheshti University.
{"title":"Comparing image segmentation methods using data envelopment analysis","authors":"Hassan Bozorgmanesh","doi":"10.52547/cmcma.1.1.48","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.48","url":null,"abstract":"In this paper, a model based on data envelopment analysis is used for comparing different image segmentation methods and also for the purpose of finding the best parameter among certain values for a method. The criteria for choosing inputs and outputs are explained and in the end, some examples are presented to demonstrate how this model works. Copyright c (cid:13) 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131121151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Samundra Regmi, I. Argyros, S. George, Christopher I. Argyros
In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study.
{"title":"On the semi-local convergence of the Homeier method in Banach space for solving equations","authors":"Samundra Regmi, I. Argyros, S. George, Christopher I. Argyros","doi":"10.52547/cmcma.1.1.63","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.63","url":null,"abstract":"In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125661154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we present two two-step methods to solve parameterized generalized inverse eigenvalue problems that appear in diverse areas of computation and engineering applications. At the (cid:12)rst step, we transfer the inverse eigenvalue problem into a system of nonlinear equations by using of the Golub-Kahan bidiagonalization. At the second step, we use Newton’s and Quasi-Newton’s methods for the numerical solution of system of nonlinear equations. Finally, we present some numerical examples which show that our methods are applicable for solving the parameterized inverse eigenvalue problems. Copyright c ⃝ 2022 Shahid Beheshti University.
{"title":"Solving parameterized generalized inverse eigenvalue problems via Golub-Kahan bidiagonalization","authors":"Zeynab Dalvand, Mohammad Ebrahim Dastyar","doi":"10.52547/cmcma.1.1.21","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.21","url":null,"abstract":"In this study, we present two two-step methods to solve parameterized generalized inverse eigenvalue problems that appear in diverse areas of computation and engineering applications. At the (cid:12)rst step, we transfer the inverse eigenvalue problem into a system of nonlinear equations by using of the Golub-Kahan bidiagonalization. At the second step, we use Newton’s and Quasi-Newton’s methods for the numerical solution of system of nonlinear equations. Finally, we present some numerical examples which show that our methods are applicable for solving the parameterized inverse eigenvalue problems. Copyright c ⃝ 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122485418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A tensor is called semi-symmetric if all modes but one, are symmetric. In this paper, we study the CP decomposition of semi-symmetric tensors or higher-order individual difference scaling (INDSCAL). Comon’s conjecture states that for any symmetric tensor, the CP rank and symmetric CP rank are equal, while it is known that Comon’s conjecture is not true in the general case but it is proved under several assumptions in the literature. In the paper, Comon’s conjecture is extended for semi-symmetric CP decomposition and CP decomposition of semi-symmetric tensors under suitable assumptions. Specially, we show that if a semi-symmetric tensor has a CP rank smaller or equal to its order, or when the semi-symmetric CP rank is less than/or equal to the dimension, then the semi-symmetric CP rank is equal to the CP rank. Copyright c (cid:13) 2022 Shahid Beheshti University.
{"title":"On rank decomposition and semi-symmetric rank decomposition of semi-symmetric tensors","authors":"Hassan Bozorgmanesh, Anthony T. Chronopoulos","doi":"10.52547/cmcma.1.1.37","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.37","url":null,"abstract":"A tensor is called semi-symmetric if all modes but one, are symmetric. In this paper, we study the CP decomposition of semi-symmetric tensors or higher-order individual difference scaling (INDSCAL). Comon’s conjecture states that for any symmetric tensor, the CP rank and symmetric CP rank are equal, while it is known that Comon’s conjecture is not true in the general case but it is proved under several assumptions in the literature. In the paper, Comon’s conjecture is extended for semi-symmetric CP decomposition and CP decomposition of semi-symmetric tensors under suitable assumptions. Specially, we show that if a semi-symmetric tensor has a CP rank smaller or equal to its order, or when the semi-symmetric CP rank is less than/or equal to the dimension, then the semi-symmetric CP rank is equal to the CP rank. Copyright c (cid:13) 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127484828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Williamson’s theorem states that every real symmetric positive definite matrix A of even order can be brought to diagonal form via a symplectic T -congruence transformation. The diagonal entries of the resulting diagonal form are called the symplectic eigenvalues of A . We point at an analog of this classical result related to Hermitian positive definite matrices, *-congruences, and another class of transformation matrices, namely, pseudo-unitary matrices. This leads to the concept of pseudo-unitary (or pseudo-orthogonal, in the real case) eigenvalues of positive definite matrices. Copyright c (cid:13) 2022 Shahid Beheshti University.
{"title":"From symplectic eigenvalues of positive definite matrices to their pseudo-orthogonal eigenvalues","authors":"K. Ikramov, A. Nazari","doi":"10.52547/cmcma.1.1.17","DOIUrl":"https://doi.org/10.52547/cmcma.1.1.17","url":null,"abstract":"Williamson’s theorem states that every real symmetric positive definite matrix A of even order can be brought to diagonal form via a symplectic T -congruence transformation. The diagonal entries of the resulting diagonal form are called the symplectic eigenvalues of A . We point at an analog of this classical result related to Hermitian positive definite matrices, *-congruences, and another class of transformation matrices, namely, pseudo-unitary matrices. This leads to the concept of pseudo-unitary (or pseudo-orthogonal, in the real case) eigenvalues of positive definite matrices. Copyright c (cid:13) 2022 Shahid Beheshti University.","PeriodicalId":207178,"journal":{"name":"Computational Mathematics and Computer Modeling with Applications (CMCMA)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125985486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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