87 research outputs found
Archeologische Atlas van de 2 Zeeën: een grensoverschrijdend maritiem archeologisch project. Eindrapport 2009-2012
Archaeological Atlas of the 2 Seas: A cross-border maritime archaeology project. Final report 2009-212
L'Atlas archéologique des 2 Mers: Un projet d'archéologie maritime transfrontalier. Rapport final 2009-2012
A Jacobi-Davidson type method with a correction equation tailored for integral operators
The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9656-9We propose two iterative numerical methods for eigenvalue computations of large dimensional problems arising from finite approximations of integral operators, and describe their parallel implementation. A matrix representation of the problem on a space of moderate dimension, defined from an infinite dimensional one, is computed along with its eigenpairs. These are taken as initial approximations and iteratively refined, by means of a correction equation based on the reduced resolvent operator and performed on the moderate size space, to enhance their quality. Each refinement step requires the prolongation of the correction equation solution back to a higher dimensional space, defined from the infinite dimensional one. This approach is particularly adapted for the computation of eigenpair approximations of integral operators, where prolongation and restriction matrices can be easily built making a bridge between coarser and finer discretizations. We propose two methods that apply a Jacobi–Davidson like correction: Multipower Defect-Correction (MPDC), which uses a single-vector scheme, if the eigenvalues to refine are simple, and Rayleigh–Ritz Defect-Correction (RRDC), which is based on a projection onto an expanding subspace. Their main advantage lies in the fact that the correction equation is performed on a smaller space while for general solvers it is done on the higher dimensional one. We discuss implementation and parallelization details, using the PETSc and SLEPc packages. Also, numerical results on an astrophysics application, whose mathematical model involves a weakly singular integral operator, are presented.This work was partially supported by European Regional Development Fund through COMPETE, FCT-Fundacao para a Ciencia e a Tecnologia through CMUP-Centro de Matematica da Universidade do Porto and Spanish Ministerio de Ciencia e Innovacion under projects TIN2009-07519 and AIC10-D-000600.Vasconcelos, PB.; D'almeida, FD.; Román Moltó, JE. (2013). A Jacobi-Davidson type method with a correction equation tailored for integral operators. Numerical Algorithms. 64(1):85-103. doi:10.1007/s11075-012-9656-9S85103641Absil, P.A., Mahony, R., Sepulchre, R., Dooren, P.V.: A Grassmann–Rayleigh quotient iteration for computing invariant subspaces. SIAM Rev. 44(1), 57–73 (2002)Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations with Bounded Operators. Chapman and Hall, Boca Raton (2001)Ahues, M., d’Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: An L 1 refined projection approximate solution of the radiation transfer equation in stellar atmospheres. J. Comput. Appl. Math. 140(1–2), 13–26 (2002)Ahues, M., d’Almeida, F.D., Largillier, A., Vasconcelos, P.B.: Defect correction for spectral computations for a singular integral operator. Commun. Pure Appl. Anal. 5(2), 241–250 (2006)Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Society for Industrial and Applied Mathematics, Philadelphia (2000)Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 3.1, Argonne National Laboratory (2010)Chatelin, F.: Spectral Approximation of Linear Operators. SIAM, Philadelphia (2011)d’Almeida, F.D., Vasconcelos, P.B.: Convergence of multipower defect correction for spectral computations of integral operators. Appl. Math. Comput. 219(4), 1601–1606 (2012)Falgout, R.D., Yang, U.M.: Hypre: A library of high performance preconditioners. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) Computational Science - ICCS 2002, International Conference, Amsterdam, The Netherlands, April 21–24, 2002. Proceedings, Part III, Lecture Notes in Computer Science, vol. 2331, pp. 632–641. Springer (2002)Henson, V.E., Yang, U.M.: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Appl. Numer. Math. 41(1), 155–177 (2002)Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)Hernandez, V., Roman, J.E., Tomas, A., Vidal, V.: SLEPc Users Manual. Tech. Rep. DSIC-II/24/02 - Revision 3.1, D. Sistemas Informáticos y Computación, Universidad Politécnica de Valencia (2010)Saad, Y.: Iterative methods for sparse linear systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)Simoncini, V., Eldén, L.: Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 42(1), 159–182 (2002)Sleijpen, G.L.G., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM Rev. 42(2), 267–293 (2000)Sorensen, D.C.: Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357–385 (1992)Stewart, G.W.: A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001
Sequence Defined Disulfide-Linked Shuttle for Strongly Enhanced Intracellular Protein Delivery
Intracellular protein transduction technology is opening the door for a promising alternative to gene therapy. Techniques have to address all critical steps, like efficient cell uptake, endolysosomal escape, low toxicity, while maintaining full functional activity of the delivered protein. Here, we present the use of a chemically precise, structure defined three-arm cationic oligomer carrier molecule for protein delivery. This carrier of exact and low molecular weight combines good cellular uptake with efficient endosomal escape and low toxicity. The protein cargo is covalently attached by a bioreversible disulfide linkage. Murine 3T3 fibroblasts could be transduced very efficiently with cargo nlsEGFP, which was tagged with a nuclear localization signal. We could show subcellular delivery of the nlsEGFP to the nucleus, confirming cytosolic delivery and expected subsequent subcellular trafficking. Transfection efficiency was concentration-dependent in a directly linear mode and 20-fold higher in comparison with HIV-TAT-nlsEGFP containing a functional TAT transduction domain. Furthermore, β-galactosidase as a model enzyme cargo, modified with the carrier oligomer, was transduced into neuroblastoma cells in enzymatically active form
A new algorithm for computing the Geronimus transformations for large shifts
A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. The basic Geronimus transformation with shift ? transforms the monic Jacobi matrix associated with a measure d? into the monic Jacobi matrix associated with d?/(x????)?+?C?(x????), for some constant C. In this paper we examine the algorithms available to compute this transformation and we propose a more accurate algorithm, estimate its forward errors, and prove that it is forward stable. In particular, we show that for C?=?0 the problem is very ill-conditioned, and we present a new algorithm that uses extended precision
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