Trading off Parallelism and Numerical Stability

نویسندگان

  • C. Lawson
  • R. Hanson
  • D. Kincaid
  • F. Krogh
چکیده

[80] K. Veseli c. A quadratically convergent Jacobi-like method for real matrices with complex conjugate eigenvalues. [82] D. Watkins and L. Elsner. Convergence of algorithms of decomposition type for the eigenvalue problem. [83] Zhonggang Zeng. Homotopy-determinant algorithm for solving matrix eigenvalue problems and its parallelizations. [69] G. Shro. A parallel algorithm for the eigenvalues and eigenvectors of a general complex matrix. [57] T.-Y. Li and Z. Zeng. Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems. [59] CC. Lin and E. Zmijewski. A parallel algorithm for computing the eigenvalues of an unsymmetric matrix on an SIMD mesh of processors. [61] M.H.C. Pardekooper. A quadratically convergent parallel Jacobi process for diagonally dominant matrices with distinct eigenvalues. [45] G. A. Geist and G. J. Davis. Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed memory multiprocessor. [48] Ming Gu and S. Eisenstat. A stable and ecient algorithm for the rank-1 modication of the symmetric eigenproblem. [52] E. Jessup. A case against a divide and conquer approach to the nonsym-metric eigenproblem. [54] E. Jessup and D Sorensen. A divide and conquer algorithm for computing the singular value decomposition of a matrix. [38] P. Eberlein. A Jacobi method for the automatic computation of eigen-values and eigenvectors of an arbitrary matrix. [43] G. A. Geist. Parallel tridiagonalization of a general matrix using distributed memory multiprocessors. [24] J. Demmel. The probability that a numerical analysis problem is di-cult. [30] J. Demmel and K. Veseli c. Jacobi's method is more accurate than QR. and eigenvectors of a general matrix by reduction to tridiagonal form. 21 [7] Z. Bai and J. Demmel. Design of a parallel nonsymmetric eigenroutine toolbox. [10] J. Barlow. Error analysis of update methods for the symmetric eigen-value problem. [11] D. Bini and D. Lotti. Stability of fast algorithms for matrix multiplication. [14] R. P. Brent. Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd's identity. 20 slow to be useful. The LAPACK 2 project will produce codes assuming reasonably ecient exception handling, since this is the most common kind of implementation [4].

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Trading off Parallelism and Numerical Stability

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تاریخ انتشار 1992