By Christian Ullrich, Jürgen Wolff von Gudenberg
The foremost objectives of the ESPRIT undertaking 1072, DIAMOND (Development and Integration of exact Mathematical Operations in Numerical Data-Processing), have been to advance a collection of actual numerical algorithms (work package deal three) and to supply instruments to help their implementation by way of embedding exact mathematics into programming languages (work package deal 1) and through transformation strategies which both increase the accuracy of expression evaluate or observe and cast off presumable deficiencies in accuracy in present courses (work package deal 2). the current quantity as a rule summarizes the result of paintings package deal 2. It contains examine papers concerning the improvement and the implementation of self-validating algorithms which instantly confirm the result of a numerical computation. Algorithms for the answer of eigenvalue/eigenvector difficulties, linear structures for sparse matrices, nonlinear platforms and quadrature difficulties, in addition to computation of zeros of a posh polynomial are provided. The algorithms continually bring assured effects, i.e. the real result's enclosed into sharp bounds.
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Extra info for Accurate Numerical Algorithms. A Collection of Research Papers
2 describes the VIPX algorithm. CM A and RB format A will occupy array A with LDA = mMB where m = ∈M/MB≈; see Sect. 1 where this layout padding was mentioned as being important. In  we improved the speed of the VIPX algorithm by using a number theory algorithm to ﬁnd, a priori, the exact nature of the vector P mapping. G. Gustavson The VIPX Vector Transpose Algorithm We overview how one gets from standard CM format to RB format. Recall, from Sect. 1, array B holds an m by NB submatrix C whose elements are column vectors of length MB.
After completion of these n parallel computation steps we have transformed CM matrix A in array A in-place to become the same matrix A but now A is represented in RB format in array A. Thus, after vector in-place transpose we have “cache blocked” matrix A! In conclusion, we hope the reader now clearly sees at a deeper level why NDS signiﬁcantly improves MC DLA algorithm performance. The transformation of A in standard format to RB format by in-place vector transposition was orders of magnitude faster than ordinary scalar in-place methods.
Eﬃcient scalable algorithms for hierarchically semiseparable matrices. SIAM J. Sci. Comput. de Abstract. Many scientiﬁc applications require the computation of about 10–30 % of the eigenvalues and eigenvectors of large dense symmetric or complex hermitian matrices. In this paper we will present performance evaluation results of the eigensolvers of the three libraries Elemental, ELPA, and ScaLAPACK on the BlueGene/Q architecture. All libraries include solvers for the computation of only a part of the spectrum.
Accurate Numerical Algorithms. A Collection of Research Papers by Christian Ullrich, Jürgen Wolff von Gudenberg