Restrictions on implicit filtering techniques for orthogonal projection methods

AbstractWe consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. Examples of OPMs are the Arnoldi and the Davidson method. We show how an OPM can be restarted — implicitly and explicitly. This restart can be used to remove a specific subset of vectors from the approximation subspace. This is called explicit filtering. An implicit restart can also be combined with an implicit filtering step, i.e. the application of a polynomial or rational function on the subspace, even if inaccurate arithmetic is assumed. However, the condition for the implicit application of a filter is that the rank of the residual matrix must be small

Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

The final publication is available at Springer via http://dx.doi.org/ 10.1007/s10543-016-0601-5.We investigate how to adapt the Q-Arnoldi method for the case of symmetric quadratic eigenvalue problems, that is, we are interested in computing a few eigenpairs of with M, C, K symmetric matrices. This problem has no particular structure, in the sense that eigenvalues can be complex or even defective. Still, symmetry of the matrices can be exploited to some extent. For this, we perform a symmetric linearization , where A, B are symmetric matrices but the pair (A, B) is indefinite and hence standard Lanczos methods are not applicable. We implement a symmetric-indefinite Lanczos method and enrich it with a thick-restart technique. This method uses pseudo inner products induced by matrix B for the orthogonalization of vectors (indefinite Gram-Schmidt). The projected problem is also an indefinite matrix pair. The next step is to write a specialized, memory-efficient version that exploits the block structure of A and B, referring only to the original problem matrices M, C, K as in the Q-Arnoldi method. This results in what we have called the Q-Lanczos method. Furthermore, we define a stabilized variant analog of the TOAR method. We show results obtained with parallel implementations in SLEPc.This work was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2013-41049-P. Carmen Campos was supported by the Spanish Ministry of Education, Culture and Sport through an FPU Grant with reference AP2012-0608.Campos, C.; Román Moltó, JE. (2016). Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems. BIT Numerical Mathematics. 56(4):1213-1236. https://doi.org/10.1007/s10543-016-0601-5S12131236564Bai, Z., Su, Y.: SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. 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Defensin-Like ZmES4 Mediates Pollen Tube Burst in Maize via Opening of the Potassium Channel KZM1

Species-preferential osmotic pollen tube burst and sperm discharge in maize involve induced opening of the pollen tube-expressed potassium channel KZM1 by the egg apparatus-derived defensin-like protein ZmES4

Study track dependent values and exam results for master students in Engineering Technology

In Belgium one distinguishes two types of bachelor degrees: the professional and the academic bachelor. A professional bachelor degree focuses on professional training (such as nursing and teaching) and does not grant automatic access to a master’s program. The goal of an academic bachelor degree on the other hand is to get all the necessary knowledge and skills to start a master’s program. However professional bachelors are not excluded from a master programme, they can start a master programme after succeeding a bridging programme. In this paper we focus on possible differences in values and skills between these two types of master students: the ones who enter the master programme by means of an academic bachelor degree (regular students) and those who got admittance after finishing a bridging programme (bridging students). In practice, the professors experience no differences. Our research reveals a significant difference between the two populations in some aspects.status: publishe

Update on therapy of relapsed and refractory multiple myeloma

The prognosis for multiple myeloma patients has improved substantially over the past decade with the development of more effective chemotherapeutic agents and regimens that possess a high level of anti-tumour activity. However, nearly all multiple myeloma patients ultimately relapse, even those who experience a complete response to initial therapy. Management of relapsed disease remains a critical aspect of multiple myeloma care and an important area of ongoing research. This manuscript from the Belgian Haematology Society multiple myeloma subgroup provides some recommendations on the management of relapsed disease