Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200010
Z. Wan, Liuyang Yuan, Jiawei Chen
In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.
{"title":"A filled function method for nonlinear systems of equalities and inequalities","authors":"Z. Wan, Liuyang Yuan, Jiawei Chen","doi":"10.1590/S1807-03022012000200010","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200010","url":null,"abstract":"In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into an equivalent constrained global optimization problem. Subsequently, a new filled function with one parameter is constructed based on the special characteristics of the reformulated optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function algorithm. The implementation of the algorithm on several test problems is reported with numerical results. Mathematical subject classification: 65K05, 90C30.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"115 1","pages":"391-405"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79497817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-28DOI: 10.1590/S1807-03022012000200009
K. Maleknejad, M. Nosrati, E. Najafi
An effective technique upon linear B-spline wavelets has been developed for solving weakly singular Fredholm integral equations. Properties of these wavelets and some operational matrices are first presented. These properties are then used to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples. Mathematical subject classification: 45A05, 32A55, 34A25, 65T60.
{"title":"Wavelet Galerkin method for solving singular integral equations","authors":"K. Maleknejad, M. Nosrati, E. Najafi","doi":"10.1590/S1807-03022012000200009","DOIUrl":"https://doi.org/10.1590/S1807-03022012000200009","url":null,"abstract":"An effective technique upon linear B-spline wavelets has been developed for solving weakly singular Fredholm integral equations. Properties of these wavelets and some operational matrices are first presented. These properties are then used to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples. Mathematical subject classification: 45A05, 32A55, 34A25, 65T60.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"148 1","pages":"373-390"},"PeriodicalIF":2.6,"publicationDate":"2012-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77793073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-04-13DOI: 10.1590/S1807-03022012000100010
R. Katani, S. Shahmorad
In this paper, we propose an efficient numerical method for solving systems of linear and nonlinear integral equations of the first and second kinds, which avoids the need for special starting values. The method has also the advantages of simplicity of application and at least six order of convergence. A convergence analysis is given and accuracy of the method is clarified by numerical examples. Mathematical subject classification: 65R20.
{"title":"A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations","authors":"R. Katani, S. Shahmorad","doi":"10.1590/S1807-03022012000100010","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100010","url":null,"abstract":"In this paper, we propose an efficient numerical method for solving systems of linear and nonlinear integral equations of the first and second kinds, which avoids the need for special starting values. The method has also the advantages of simplicity of application and at least six order of convergence. A convergence analysis is given and accuracy of the method is clarified by numerical examples. Mathematical subject classification: 65R20.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"11 1","pages":"191-203"},"PeriodicalIF":2.6,"publicationDate":"2012-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88801759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-04-13DOI: 10.1590/S1807-03022012000100008
J. Lima, Francisco M. Silva, E. Villareal
This work introduces a new data transmission system in which the main blocks, coding, modulation and channel are designed on a Riemannian manifolds. An intrinsic algebraic structure to the manifolds (surface), the homology group will be used to compose an error corrector code, a partition on the surface extracted from the embedding of a graph, which will compose the modulation design, and the channel design is the result of an association rule applied to the embedded graph. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
{"title":"A new approach for data transmission system on topological surfaces","authors":"J. Lima, Francisco M. Silva, E. Villareal","doi":"10.1590/S1807-03022012000100008","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100008","url":null,"abstract":"This work introduces a new data transmission system in which the main blocks, coding, modulation and channel are designed on a Riemannian manifolds. An intrinsic algebraic structure to the manifolds (surface), the homology group will be used to compose an error corrector code, a partition on the surface extracted from the embedding of a graph, which will compose the modulation design, and the channel design is the result of an association rule applied to the embedded graph. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"59 1","pages":"143-168"},"PeriodicalIF":2.6,"publicationDate":"2012-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72988532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000300009
V. G. Ferreira, R. D. Queiroz, M. Candezano, G. A. B. Lima, L. Corrêa, C. Oishi, F. L. P. Santos
This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
{"title":"Simulation results and applications of an advection bounded scheme to practical flows","authors":"V. G. Ferreira, R. D. Queiroz, M. Candezano, G. A. B. Lima, L. Corrêa, C. Oishi, F. L. P. Santos","doi":"10.1590/S1807-03022012000300009","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300009","url":null,"abstract":"This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"1 1","pages":"591-616"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88776721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000100006
Z. Makukula, P. Sibanda, S. Motsa
The steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipationis studied. We present a novel technique for accelerating the convergence of the spectral-homotopy analysis method. Solutions of the nonlinear momentum and energy equations are obtained using the improved spectral homotopy analysis method. Solutions were also generated using the spectral-homotopy analysis method and benchmarked against results in the literature. Mathematical subject classification: Primary: 76A05, 76N05; Secondary: 76M25.
{"title":"On a linearisation method for Reiner-Rivlin swirling flow","authors":"Z. Makukula, P. Sibanda, S. Motsa","doi":"10.1590/S1807-03022012000100006","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100006","url":null,"abstract":"The steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipationis studied. We present a novel technique for accelerating the convergence of the spectral-homotopy analysis method. Solutions of the nonlinear momentum and energy equations are obtained using the improved spectral homotopy analysis method. Solutions were also generated using the spectral-homotopy analysis method and benchmarked against results in the literature. Mathematical subject classification: Primary: 76A05, 76N05; Secondary: 76M25.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"476 1","pages":"95-125"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86748087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000300010
F. Louzada, V. Cancho, Gladys D. C. Barriga
In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activationschemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer. Mathematical subject classification: 62N01, 62N99.
{"title":"The Poisson-exponential regression model under different latent activation schemes","authors":"F. Louzada, V. Cancho, Gladys D. C. Barriga","doi":"10.1590/S1807-03022012000300010","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300010","url":null,"abstract":"In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activationschemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer. Mathematical subject classification: 62N01, 62N99.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"13 1","pages":"617-632"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87291171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000100011
Rodrigo Garcés, Walter Gómez, F. Jarre
In this short note a sensitivity result for quadratic semidefinite programming is presented under a weak form of second order sufficient condition. Based on this result, also the local convergence of a sequential quadratic semidefinite programming algorithm extends to this weak second order sufficient condition. Mathematical subject classification: 90C22, 90C30, 90C31, 90C55.
{"title":"A sensitivity result for quadratic semidefinite programs with an application to a sequential quadratic semidefinite programming algorithm","authors":"Rodrigo Garcés, Walter Gómez, F. Jarre","doi":"10.1590/S1807-03022012000100011","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100011","url":null,"abstract":"In this short note a sensitivity result for quadratic semidefinite programming is presented under a weak form of second order sufficient condition. Based on this result, also the local convergence of a sequential quadratic semidefinite programming algorithm extends to this weak second order sufficient condition. Mathematical subject classification: 90C22, 90C30, 90C31, 90C55.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"77 1","pages":"205-218"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85916221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000100004
Min Li, Heying Feng, Jianguo Liu
Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.
{"title":"The global convergence of a descent PRP conjugate gradient method","authors":"Min Li, Heying Feng, Jianguo Liu","doi":"10.1590/S1807-03022012000100004","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100004","url":null,"abstract":"Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"15 1","pages":"59-83"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78477572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1590/S1807-03022012000100001
Shouting Chen, Ruguang Zhou
An integrable decomposition of the Manakov equation is presented. A pair of new finite-dimensional integrable Hamiltonian systems which constitute the integrable decomposition of the Manakov equation are obtained. Mathematical subject classification: 37K10.
{"title":"An integrable decomposition of the Manakov equation","authors":"Shouting Chen, Ruguang Zhou","doi":"10.1590/S1807-03022012000100001","DOIUrl":"https://doi.org/10.1590/S1807-03022012000100001","url":null,"abstract":"An integrable decomposition of the Manakov equation is presented. A pair of new finite-dimensional integrable Hamiltonian systems which constitute the integrable decomposition of the Manakov equation are obtained. Mathematical subject classification: 37K10.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"9 1","pages":"01-18"},"PeriodicalIF":2.6,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73085806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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