James W. Demmel, Michael T. Heath, and Henk A. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica, pages 111{ 197. Cambridge University Press, England, 1993. Home/Search Document Details and Download
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The Homotopy Method Applied to the Symmetric Eigenproblem - Oettli (1995) (1 citation) (Correct)
....QR iteration for finding the eigenvalues of a symmetric tridiagonal matrix must be done sequentially with usually just one eigenvalue converging at a time. Thus, it is not suitable for parallel computers. However, when computing the eigenvector matrix Q too, it is especially easy to parallelize [7, 26]. Each processor redundantly runs the entire algorithm updating the tridiagonal matrix by forming PAP , but only computes n=p of the columns of PQ, where p is the number of processors and n is the dimension of A. At the end each processor has all eigenvalues and n=p components of each ....
J. W. Demmel and M. T. Heath. Parallel numerical linear algebra. Acta Numerica, 1993.
Recent Developments in Dense Numerical Linear Algebra - Higham (2000) (Correct)
.... generalized eigenproblem; see [9] 10] Condition numbers and error bounds for the generalized eigenproblem and algorithms for reordering the generalized Schur form are given by Kagstrom and Poromaa [95] A comprehensive survey of existing parallel eigenroutines and their limitations is given in [39]. 6 The Symmetric Eigenvalue Problem An important recent development in solution of the symmetric eigenproblem concerns a divide and conquer algorithm for tridiagonal matrices. The algorithm writes a symmetric tridiagonal T in the form T 11 0 0 T 22 where only the trailing diagonal element ....
James W. Demmel, Michael T. Heath, and Henk A. van der Vorst. Parallel numerical linear algebra. In Acta Numerica, Cambridge University Press, 1993, pages 111--198.
FORSCHUNGSZENTRUM JLICH GmbH - Zentralinstitut Ftir Angewandte (Correct)
....and sscal: call sscal(n k,one a(k,k) a(k l,k) l) call sger(n k,n k, one, a(k l,k) 1, a(k,k l) n,a(k l,k l) n) 12 This code is used in the level 2 BLAS version of the LAPACK LU decomposition routine sgetf2. To convert to a level 3 BLAS version column blocking of the matrix A is used ([5]) so let A= AA2. A) An A2 . Am ) A.2 A22 A2 k,A A2 . A with m column blocks A i consisting of m quadratic submatrices Aik of the same dimension (this is called the block size) and equivalent Ln 0 . 0 ) L.2 L22 . 0 Lml Lm2 . Lmm U22 S2m : 0 . Umm which ....
....similar tridiagonal matrices Ai converging to diagonal form. Each iteration step can be viewed as pre and postmultiplication with n 1 plane rotations (Givens rotation) Once taking advantage of the symmetric tridiagonal form of A this becomes a nonlinear recurrence, which is not parallelizable ([5]) Alternative approaches like divide and conquer method or multisectioning algorithms potentially offer more scope for parallelism ( 7] 5.2 Test example and subroutines used Only the eigenvalues of a real symmetric matrix were investigated here. The real nonsymmetric eigen 26 value problem ....
J.W. Demmel, M.T. Heath and N.A. van der Vorst, Parallel numerical linear algebra, LAPACK Working Note 60, UT CS-93-192, August 1993.
Parallel Implementation of Fast Wavelet Transforms - Ford, Chen, Ford (2001) (Correct)
....processing has become a realistic option for a wider range of users employing a greater variety of hardware, for example using a cluster of PCs. To take full advantage of these new opportunities parallel algorithms need to be able to utilise whatever number of processors is available. See [6] for a discussion of the importance of designing algorithms that are not restricted to speci c architectures and matrix sizes. Here we present algorithms for the parallel computation of a 2 D wavelet transform using arbitrary number of processors and matrix size. 1.1 Fast Wavelet Transforms A ....
James W. Demmel, Michael T. Heath, and Henk A. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica (
Parallel Krylov Methods for Econometric Model Simulation - Pauletto, Gilli (2000) (Correct)
....that a parallel environment is the researcher s most important companion for computationally intensive tasks. 2 Important Issues in Parallel Programming To some extent, the problems encountered with parallel programming can be compared to those that early serial programmers faced. According to Demmel et al. 1993), programmers of current serial machines can ignore many of the details 1 See http: beowulf.gsfc.nasa.gov for a description of the Beowulf project. 2 that earlier programmers could ignore only at the risk of significantly slower programs. With modern parallel computers, once again we must be ....
.... y i = ffx i y i ; i = 1; n 2n 3n 1 2=3 matrix Theta vector y i = P n j=1 a ij x j y i 2n 2 n 2 3n 2 matrix Theta matrix c ij = P n k=1 a ik b kj c ij 2n 3 4n 2 n=2 We see from Table 1 that only matrix matrix multiplication offers an opportunity 2 Table given in Demmel et al. 1993). 4 to increase the ratio between Flops and memory references as n grows. Hence an effective approach for designing parallel algorithms attempts to decompose the computations as much as possible into a sequence of dense matrix multiplications. 3 Sparse Direct Methods Direct methods for solving ....
Demmel, J.W., Heath, M.T. and van der Vorst, H.A., (1993). Parallel Numerical Linear Algebra. Acta Numerica, 111--197.
Application of a Class of Preconditioners to Large.. - Venansius.. (Correct)
....6= 0 then V jffl V jffl Gamma L ji V iffl R ji = L ji V jffl u Fig. 1. Updating the triangular factors either many zero rows in A or few nonzero elements in the unit lower triangular factor L. The major computation in an interior point algorithm is in solving linear systems. Demmel et al. [4] discuss parallel algorithms for conjugate gradients and computing Cholesky factors. The construction of the preconditioner (updating of the triangular factors) can be done in parallel. 4 Numerical Results Here, we give some numerical results using the same implementation details as in [2] The ....
J. W. Demmel, M.T. Heath, and H.A. Van der Vorst, Parallel numerical linear algebra, Acta Numerica, pp. 111-197, 1993.
The Instability Of Parallel Prefix Matrix Multiplication - Mathias (1997) (4 citations) (Correct)
....they have been detected, may be expensive, we will not have to use them often. 4 Our approach fits into the paradigm of computing a quantity by a fast though possibly unstable method, checking for stability, and if necessary recomputing by a slower stable method if necessary. See, for example, [3] for further discussion and other methods of this type. Another application of the formula (4.18) for the relative component wise backward error is in verifying the accuracy of a computed eigenvalue. Suppose that we use bisection combined with parallel prefix evaluation of the d i (but no checks ....
J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. Acta Numerica. (to appear).
On the Correctness of Parallel Bisection in Floating Point - James Demmel Computer (1994) (5 citations) Self-citation (Demmel) (Correct)
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J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica, volume 2. Cambridge University Press, 1993.
Inverse Free Parallel Spectral Divide and Conquer.. - For Nonsymmetric.. Self-citation (Demmel) (Correct)
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J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica, volume 2. Cambridge University Press, 1993.
On The Correctness Of Some Bisection-Like Parallel Eigenvalue.. - Demmel, al. (1995) (4 citations) Self-citation (Demmel) (Correct)
....that this cannot happen for the LAPACK routine dstebz even for general symmetric acyclic matrices. 4.2. Nonmonotonicity of Parallel Prefix Algorithm. We now give another example of a nonmonotonic FloatingCount(x) when Count(x) is implemented using a fast parallel algorithm called parallel prefix [11]. Figure 4.1 shows the FloatingCount(x) for a 6464 matrix of norm near 1 with 32 eigenvalues very close to 5 10 8 computed both by conventional bisection (FlCnt IEEE) and the parallel prefix algorithm in the neighborhood of the eigenvalues; see [21, 14] for details. 4.3. A Correct Serial ....
J. Demmel, M. Heath, and H. van der Vorst, Parallel numerical linear algebra, In A. Iserles, editor, Acta Numerica, volume 2, Cambridge University Press, 1993.
150 Years Old and Still Alive: Eigenproblems - van der Vorst, Golub (1997) (2 citations) Self-citation (Van der vorst) (Correct)
.... these eigenvalues as function of a parameter in the underlying model [43, 44] We will sketch this approach and point at some relations with other iterative methods ffl Parallelism (Cuppen s Divide and Conquer [17, 22] Restructuring of iterative algorithms in an attempt to combine innerproducts [21, 5, 20]) ffl Subspace methods for interior eigenvalues [49, 63] rational Lanczos [62, 63] harmonic Ritz values [28, 47, 55] We will discuss some of these approaches in this paper. The remainder of this paper has been organized as follows. We start with an introduction to Krylov subspace methods. ....
....methods is, except for the (approximate) shiftand invert steps, usually no big problem. For some modern computers the required innerproducts may form a bottleneck with respect to scalable performance. For an overview of techniques to improve parallel behavior of algorithms for eigenproblems, see [21]. 9 Some open problems We have highlighted some of the progress that has been made in the past period. A novice in this area might easily have got the impression that most of the rele vant problems, associated with the computation of eigenvalues and eigenvectors have been solved. Fortunately, ....
J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In Acta Numerica 1993. Cambridge University Press, Cambridge, 1993.
Closer to the solution: Iterative linear solvers - Golub, van der Vorst (1997) (15 citations) Self-citation (Van der vorst) (Correct)
....problem. Parallel computing is a very important issue in solving large linear systems, but we have treated this issue only in passing. One might easily dedicate an entire paper for highlighting developments in this area. We restrict ourselves to referring to the overview paper by Demmel et al. [29], in which parallel approaches are discussed as well as open problems in this area. Although the list of interesting open problems can be made arbitrarily longer, space limitations forced us to mention only a few of them. Acknowledgements The authors wish to thank Andy Wathen for his careful ....
J. Demmel, M. Heath, and H. Van der Vorst. Parallel numerical linear algebra. In Acta Numerica 1993. Cambridge University Press, Cambridge, 1993.
On The Correctness Of Some Bisection-Like Parallel.. - Demmel, Dhillon, al. (1995) (4 citations) Self-citation (Demmel) (Correct)
....that this cannot happen for the LAPACK routine dstebz even for general symmetric acyclic matrices. 4.2. Nonmonotonicity of Parallel Prefix Algorithm. We now give another example of a nonmonotonic FloatingCount(x) when Count(x) is implemented using a fast parallel algorithm called parallel prefix [11]. Figure 4.1 shows the FloatingCount(x) for a 64 Theta 64 matrix of norm near 1 with 32 eigenvalues very close to 5 Delta 10 Gamma8 computed both by conventional bisection (FlCnt IEEE) and the parallel prefix algorithm in the neighborhood of the eigenvalues; see [21, 14] for details. 4.3. A ....
J. Demmel, M. Heath, and H. van der Vorst, Parallel numerical linear algebra, In A. Iserles, editor, Acta Numerica, volume 2, Cambridge University Press, 1993.
Wavelet-Based Preconditioning of Dense Linear Systems - Ford (2001) (Correct)
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James W. Demmel, Michael T. Heath, and Henk A. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica, pages 111{ 197. Cambridge University Press, England, 1993.
On the Error Analysis and Implementation of Some Eigenvalue.. - Ren (1996) (Correct)
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J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In A. Iserles, editor, Acta Numerica, volume 2. Cambridge University Press, 1993. 148
Iterative Solution of Multiple Linear Systems: Theory, . . . - Gallopoulos, al. (1994) (Correct)
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J. W. DEMMEL, M. T. HEATH, AND H. A. VAN DER VORST, Parallel numerical linear algebra, in Acta Numerica
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J. W. Demmel, M. T. Heath, and H. A. v. d. Vorst. Parallel numerical linear algebra. Technical Report UCB/CSD-92-703, University of California at Berkely, October 1992.
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M. Heath J. Demmel and H. van der Vorst, Parallel Numerical Linear Algebra, Acta Numerica 1993.
Physical cloth simulation on a PC cluster - Zara, Faure, Vincent (2002) (1 citation) (Correct)
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J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In Acta Numerica 1993, pages 111--198. Cambridge University Press, Cambridge, UK, 1993.
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DEMMEL, J., HEATH, M., AND VAN DER VORST, H. Parallel numerical linear algebra. In Acta Numerica 1993.
A Parallel Version of the Unsymmetric Lanczos Algorithm and.. - Bücker, Sauren (1996) (Correct)
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J. W. Demmel, M. T. Heath, and H. A. van der Vorst. Parallel Numerical Linear Algebra. In Acta Numerica 1993.
Solving Linear Equations on Parallel Distributed Memory.. - Andersson (Correct)
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J. W. Demmel, M. T. Heath, and H. A. Van der Vorst, Parallel numerical linear algebra,tech. rep., LAPACK Working Note 60, 1993.
Implementation Aspects - For Eective Use (Correct)
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J. Demmel, M. Heath, and H. van der Vorst. Parallel numerical linear algebra. In Acta Numerica 1993.
A Class of Preconditioners for Weighted Least Squares.. - Baryamureeba, Steihaug.. (1999) (Correct)
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J.W. Demmel, M.T. Heath, and H.A. Van der Vorst, Parallel numerical linear algebra, Acta Numerica, pp. 111-197, 1993.
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DEMMEL,J.W.,HEATH,M.T.,AND VAN DER VORST, H. A. 1993. Parallel numerical linear algebra. Acta Numer. 2, 111--197.
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