The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.

A promising method for characterizing the phenotype of a plant as an interaction between its genotype and its environment is to use refined organ-scale plant growth models that use the observation of architectural traits, such as leaf area, containing a lot of information on the whole history of the functioning of the plant. The Phenoscope, a high-throughput automated platform, allowed the acquisition of zenithal images of Arabidopsis thaliana over twenty one days for 4 different genotypes. A novel image processing algorithm involving both segmentation and tracking of the plant leaves allows to extract areas of the latter. First, all the images in the series are segmented independently using a watershed-based approach. A second step based on ellipsoid-shaped leaves is then applied on the segments found to refine the segmentation. Taking into account all the segments at every time, the whole history of each leaf is reconstructed by choosing recursively through time the most probable segment achieving the best score, computed using some characteristics of the segment such as its orientation, its distance to the plant mass center and its area. These results are compared to manually extracted segments, showing a very good accordance in leaf rank and that they therefore provide low-biased data in large quantity for leaf areas. Such data can therefore be exploited to design an organ-scale plant model adapted from the existing GreenLab model for A. thaliana and subsequently parameterize it. This calibration of the model parameters should pave the way for differentiation between the Arabidopsis genotypes.

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