Showing papers on "Tridiagonal matrix algorithm published in 1977"
TL;DR: The results of Wilkinson on the stability of Gaussian elimination with column pivoting are generalized.
Abstract: The results of Wilkinson on the stability of Gaussian elimination with column pivoting are generalized.
9 citations
1 Jul 1977
TL;DR: Three relatively brief papers are presented on the following subjects: element growth in Gaussian elimination, estimating cond(A) with subroutine DGECO, and consideration of an error bound inGaussian elimination.
Abstract: Three relatively brief papers are presented on the following subjects: element growth in Gaussian elimination, estimating cond(A) with subroutine DGECO, and consideration of an error bound in Gaussian elimination. (RWR)
2 citations
1 Dec 1977
TL;DR: In this paper, a nonsingular transformation matrix T that relates the state triple (AT, BT, CT) of tridiagonal to state triple of phase canonical linear system is given.
Abstract: A nonsingular transformation matrix T that relates the state triple (AT, BT, CT) of tridiagonal to state triple (Ap,Bp,Cp) of phase canonical linear system is given. The simple rules for evaluating the entries of matrix T arc also included.
TL;DR: It is shown that if the size of the tridiagonal matrix in any given iteration is n, then the parallel QR algorithm requires 0(log2n) steps with 0(n) processors per iteration and no square roots, which results in a speedup of 0 (n/log 2n) over the sequential algorithm with an efficiency of 0(1/ log2n).
Abstract: We show that if the size of the tridiagonal matrix in any given iteration is n, then the parallel QR algorithm requires 0(log 2 n) steps with 0(n) processors per iteration and no square roots. This results in a speedup of 0(n/log 2 n) over the sequential algorithm with an efficiency of 0(1/log 2 n). We also give an error analysis of the parallel triangular system solvers used in each iteration.