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Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

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Research paper thumbnail of Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

We regret to mention that the name of Mariarosaria Rizzardi, Parthenope University, Naples, Italy... more We regret to mention that the name of Mariarosaria Rizzardi, Parthenope University, Naples, Italy was missing amongst the listed authors. The complete authors are indicated here. The paper should be referenced with the full list of authors as L. D’Amore,
R. Campagna, V. Mele, A. Murli, M. Rizzardi.

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Research paper thumbnail of Algorithm 946

ACM Transactions on Mathematical Software, 2014

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Research paper thumbnail of An Approach to Model Resources Rationalisation in Hybrid Clouds through Users Activity Characterisation

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Research paper thumbnail of On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion

Numerical Mathematics and Advanced Applications 2009, 2010

Many applications are tackled using the Laplace Transform (LT) known on a countable number of rea... more Many applications are tackled using the Laplace Transform (LT) known on a countable number of real values [J. Electroanal. Chem. 608, 37–46 (2007), Int. J. solid Struct. 41, 3653–3674 (2004), Imaging 26, 1183–1196 (2008), J. Magn. Reson. 156, 213–221 (2002)]. The usual approach to solve the LT inverse problem relies on a regularization technique combined with information a priori both on the LT function and on its inverse (see for instance [http://s-provencher.com/pages/ contin.shtml]). We propose a fitting model enjoying LT properties: we define a generalized spline that interpolates the LT function values and mimics the asymptotic behavior of LT functions. Then, we prove existence and uniqueness of this model and, through a suitable error analysis, we give a priori approximation error bounds to confirm the reliability of this approach. Numerical results are presented.

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Research paper thumbnail of Algorithm 946

ACM Transactions on Mathematical Software, 2014

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Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

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Research paper thumbnail of Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

Numerical Algorithms, 2013

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Research paper thumbnail of ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

Numerical Algorithms, 2013

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Research paper thumbnail of An efficient algorithm for regularization of Laplace transform inversion in real case

Journal of Computational and Applied Mathematics, 2007

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Research paper thumbnail of A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis

Inverse Problems, 2012

The scientific and application-oriented interest in the Laplace transform and its inversion is te... more The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has

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Research paper thumbnail of A PETSc Based Parallel Software for Simulations of the Dynamics of Viscoelastic Flows

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Research paper thumbnail of Algorithm 946: ReLIADiff—A C++ Software Package for Real Laplace Transform Inversion based on Algorithmic Differentiation

Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is ... more Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used for calculating function values of the inverse Laplace transform. The software requires transform values at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented
in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article, we present
ReLIADiff focusing on its design principles, performance, and use.

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Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

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Research paper thumbnail of Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

We regret to mention that the name of Mariarosaria Rizzardi, Parthenope University, Naples, Italy... more We regret to mention that the name of Mariarosaria Rizzardi, Parthenope University, Naples, Italy was missing amongst the listed authors. The complete authors are indicated here. The paper should be referenced with the full list of authors as L. D’Amore,
R. Campagna, V. Mele, A. Murli, M. Rizzardi.

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Research paper thumbnail of Algorithm 946

ACM Transactions on Mathematical Software, 2014

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Research paper thumbnail of An Approach to Model Resources Rationalisation in Hybrid Clouds through Users Activity Characterisation

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Research paper thumbnail of On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion

Numerical Mathematics and Advanced Applications 2009, 2010

Many applications are tackled using the Laplace Transform (LT) known on a countable number of rea... more Many applications are tackled using the Laplace Transform (LT) known on a countable number of real values [J. Electroanal. Chem. 608, 37–46 (2007), Int. J. solid Struct. 41, 3653–3674 (2004), Imaging 26, 1183–1196 (2008), J. Magn. Reson. 156, 213–221 (2002)]. The usual approach to solve the LT inverse problem relies on a regularization technique combined with information a priori both on the LT function and on its inverse (see for instance [http://s-provencher.com/pages/ contin.shtml]). We propose a fitting model enjoying LT properties: we define a generalized spline that interpolates the LT function values and mimics the asymptotic behavior of LT functions. Then, we prove existence and uniqueness of this model and, through a suitable error analysis, we give a priori approximation error bounds to confirm the reliability of this approach. Numerical results are presented.

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Research paper thumbnail of Algorithm 946

ACM Transactions on Mathematical Software, 2014

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Research paper thumbnail of Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Applied Mathematics and Computation, 2015

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Research paper thumbnail of Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

Numerical Algorithms, 2013

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Research paper thumbnail of ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

Numerical Algorithms, 2013

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Research paper thumbnail of An efficient algorithm for regularization of Laplace transform inversion in real case

Journal of Computational and Applied Mathematics, 2007

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Research paper thumbnail of A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis

Inverse Problems, 2012

The scientific and application-oriented interest in the Laplace transform and its inversion is te... more The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has

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Research paper thumbnail of A PETSc Based Parallel Software for Simulations of the Dynamics of Viscoelastic Flows

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Algorithm 946: ReLIADiff—A C++ Software Package for Real Laplace Transform Inversion based on Algorithmic Differentiation

Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is ... more Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used for calculating function values of the inverse Laplace transform. The software requires transform values at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented
in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article, we present
ReLIADiff focusing on its design principles, performance, and use.

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