The Experts below are selected from a list of 3507 Experts worldwide ranked by ideXlab platform
Ichizo Ninomiya - One of the best experts on this subject based on the ideXlab platform.
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980 ) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991 ; ACM Trans. Math. Softw. 17:218–232, 1991 ). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971 ).
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (1980) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (1971)
N. A. Zadorin - One of the best experts on this subject based on the ideXlab platform.
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An analogue of the four-point Newton-Cotes formula for a function with a boundary-layer component
Numerical Analysis and Applications, 2013Co-Authors: A. I. Zadorin, N. A. ZadorinAbstract:The construction of the Newton-Cotes formulas is based on approximating the integrand by a Lagrange polynomial. The error of such quadrature formulas can be great for a function with a boundary-layer component. In this paper, an analog of the four-point Newton-Cotes Rule is constructed. The construction is based on using a nonpolynomial interpolation that is exact for the boundary layer component. Error estimates of the quadrature Rule independent of the boundary layer component gradients are obtained. Numerical experiments are performed.
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NAA - Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component
Lecture Notes in Computer Science, 2013Co-Authors: A. I. Zadorin, N. A. ZadorinAbstract:Quadrature formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes quadrature formulas leads to large errors. An analogue of Newton-Cotes Rule with five nodes is constructed. The error of the constructed formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.
Takemitsu Hasegawa - One of the best experts on this subject based on the ideXlab platform.
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980 ) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991 ; ACM Trans. Math. Softw. 17:218–232, 1991 ). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971 ).
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (1980) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (1971)
A. I. Zadorin - One of the best experts on this subject based on the ideXlab platform.
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An analogue of the four-point Newton-Cotes formula for a function with a boundary-layer component
Numerical Analysis and Applications, 2013Co-Authors: A. I. Zadorin, N. A. ZadorinAbstract:The construction of the Newton-Cotes formulas is based on approximating the integrand by a Lagrange polynomial. The error of such quadrature formulas can be great for a function with a boundary-layer component. In this paper, an analog of the four-point Newton-Cotes Rule is constructed. The construction is based on using a nonpolynomial interpolation that is exact for the boundary layer component. Error estimates of the quadrature Rule independent of the boundary layer component gradients are obtained. Numerical experiments are performed.
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NAA - Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component
Lecture Notes in Computer Science, 2013Co-Authors: A. I. Zadorin, N. A. ZadorinAbstract:Quadrature formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes quadrature formulas leads to large errors. An analogue of Newton-Cotes Rule with five nodes is constructed. The error of the constructed formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.
Susumu Hibino - One of the best experts on this subject based on the ideXlab platform.
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980 ) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991 ; ACM Trans. Math. Softw. 17:218–232, 1991 ). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971 ).
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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes
Numerical Algorithms, 2007Co-Authors: Takemitsu Hasegawa, Susumu Hibino, Yohsuke Hosoda, Ichizo NinomiyaAbstract:An improvement is made to an automatic quadrature due to Ninomiya (1980) of adaptive type based on the Newton–Cotes Rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (1971)