The Scilab Language

Gomez, Claude; Bunks, Carey; Chancelier, Jean-Philippe; Delebecque, F.; Goursat, Maurice; Nikoukhah, Ramine; Steer, S.

doi:10.1007/978-1-4612-1584-4_2

Cited by 6 publications

(7 citation statements)

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“…The computer code for general nonlinear equation system resolution by an iterative method was borrowed from the publicly available Scilab source code . The SYNAPS library was used to specifically solve polynomial equation sets by means of symbolic computations .…”

Section: Resultsmentioning

confidence: 99%

Anion-Exchange Displacement Centrifugal Partition Chromatography

et al. 2004

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Ion-exchange displacement chromatography has been adapted to centrifugal partition chromatography. The use of an ionic liquid, benzalkonium chloride, as a strong anion-exchanger has proven to be efficient for the preparative separation of phenolic acid regioisomers. Multigram quantities of a mixture of three hydroxycinnamic acid isomers were separated using iodide as a displacer. The displacement process was characterized by a trapezoidal profile of analyte concentration in the eluate with narrow transition zones. By taking advantage of the partition rules involved in support-free liquid-liquid chromatography, a numerical separation model is proposed as a tool for preliminary process validation and further optimization.

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Section: Resultsmentioning

confidence: 99%

Anion-Exchange Displacement Centrifugal Partition Chromatography

et al. 2004

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“…All the numerical experiments are carried out with the numerical software Scilab (Gomez et al, 1999). We use the Mersenne Twister pseudo random number generator of M. Matsumoto and T. Nishimura, which is the default pseudo random number generator in Scilab for large-size random simulations.…”

Section: Numerical Results For the Variance Hyper-parameter Estimationmentioning

confidence: 99%

Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification

Bachoc

2013

Computational Statistics & Data Analysis

172

141

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The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the estimation of a single variance hyper-parameter is addressed, for which the fixed correlation function is misspecified. A predictive variance based quality criterion is introduced and a closed-form expression of this criterion is derived. It is shown that when the correlation function is misspecified, the CV does better compared to ML, while ML is optimal when the model is well-specified. In the second step, the results of the first step are extended to the case when the hyper-parameters of the correlation function are also estimated from data.

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“…Of course, the algorithm of Section 3.2 can be very easily adapted if one wants to restrict the computation of the first excited state to a particular symmetry. The results presented in the following sections have been obtained with a Scilab [67] program, interfaced with a few C routines aiming in particular at speeding up the tensor-matrix products (22). Let us mention that the overlap matrices S, the core Hamiltonians h, and the bielectronic integral tensors W have been extracted from Gaussian 98 calculations [68].…”

Section: Numerical Results: the H 2 Moleculementioning

confidence: 99%

Computing electronic structures: A new multiconfiguration approach for excited states

Cancès

Galicher

Lewin

2006

Journal of Computational Physics

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We present a new method for the computation of electronic excited states of molecular systems. This method is based upon a recent theoretical definition of multiconfiguration excited states [due to one of us, see M. Lewin, Solutions of the multiconfiguration equations in quantum chemistry, Arch. Rat. Mech. Anal. 171 (2004) 83-114]. Our algorithm, dedicated to the computation of the first excited state, always converges to a stationary state of the multiconfiguration model, which can be interpreted as an approximate excited state of the molecule.The definition of this approximate excited state is variational. An interesting feature is that it satisfies a non-linear Hylleraas-Undheim-MacDonald type principle: the energy of the approximate excited state is an upper bound to the true excited state energy of the N-body Hamiltonian.To compute the first excited state, one has to deform paths on a manifold, like this is usually done in the search for transition states between reactants and products on potential energy surfaces. We propose here a general method for the deformation of paths which could also be useful in other settings.We also compare our method to other approaches used in Quantum Chemistry and give some explanation of the unsatisfactory behaviours which are sometimes observed when using the latters.Numerical results for the special case of two-electron systems are provided: we compute the first singlet excited state potential energy surface of the H 2 molecule.

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The Scilab Language

Cited by 6 publications

References 0 publications

Anion-Exchange Displacement Centrifugal Partition Chromatography

Anion-Exchange Displacement Centrifugal Partition Chromatography

Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification

Computing electronic structures: A new multiconfiguration approach for excited states

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