Now showing items 1-5 of 5

    • Bounding the Error in Gaussian Elimination for Tridiagonal Systems 

      Higham, Nicholas J. (Cornell University, 1988-12)
      If $\hat{x}$ is the computed solution to a tridiagonal system $Ax = b$ obtained by Gaussian elimination, what is the "best" bound available for the error $x - \hat{x}$ and how can it be computed efficiently? This question ...
    • A Collection of Test Matrices in MATLAB 

      Higham, Nicholas J. (Cornell University, 1989-07)
      We present a collection of forty-four parametrized test matrices. The matrices are mostly square, dense, nonrandom, and of arbitrary dimension. The collection includes matrices with known inverses or known eigenvalues; ...
    • Exploiting Fast Matrix Multiplication Within the Level 3 BLAS 

      Higham, Nicholas J. (Cornell University, 1989-04)
      The Level 3 BLAS (BLAS3) are a set of specifications of Fortran 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple right-hand sides. They are intended to provide ...
    • Fast Polar Decomposition of an Arbitrary Matrix 

      Higham, Nicholas J.; Schreiber, Robert S. (Cornell University, 1988-10)
      The polar decomposition of an $m x n$ matrix $A$ of full rank, where $m \geq n$, can be computed using a quadratically convergent algorithm of Higham [SIAM J. Sci. Stat. Comput., 7 (1986), pp.1160-1174]. The algorithm ...
    • How Accurate is Gaussian Elimination? 

      Higham, Nicholas J. (Cornell University, 1989-07)
      J.H. Wilkinson put Gaussian elimination (GE) on a sound numerical footing in the 1960's when he showed that with partial pivoting the method is stable in the sense of yielding a small backward error. He also derived ...