• Corpus ID: 122814683

Introduction to matrix computations

@inproceedings{Stewart1973IntroductionTM,
  title={Introduction to matrix computations},
  author={G. W. Stewart},
  year={1973}
}
Preliminaries. Practicalities. The Direct Solution of Linear Systems. Norms, Limits, and Condition Numbers. The Linear Least Squares Problem. Eigenvalues and Eigenvectors. The QR Algorithm. The Greek Alphabet and Latin Notational Correspondents. Determinants. Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination. Of Things Not Treated. Bibliography. Index. 
The decompositional approach to matrix computation
TLDR
The article outlines the decompositional approach, comments on its history, and surveys the six most widely used decompositions: Cholesky decomposition; pivoted LU decomposition.
Stable LU factorization of H-matrices
Solving linear systems on a vector computer
Cyclicity in multicompanion canonical matrices
A simple approach to the computation of the minimal polynomial and of eigenvectors of Luenberger controllable canonical forms is presented. The algorithm is useful when there are defective
An efficient algorithm for computing powers of triangular matrices
An efficient algorithm for the computation of powers of a square arbitrary lower triangular matrix is presented. A comparison of the algorithm with the standard matrix multiplication method in terms
Two Hadamard numbers for matrices
A discussion is given of two functions of the entries of a square matrix, both related to Hadamard's determinant theorem, which have some merits as alternatives to norm-bound “condition numbers.” One
Stability of fast algorithms for structured linear systems
  • R. Brent
  • Computer Science, Mathematics
    ArXiv
  • 2010
TLDR
This work surveys the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure and considers algorithms which incorporate pivoting without destroying the structure.
Parallel complexities and computations of cholesky's decomposition and QR factorization
In this paper, it is shown that the parallel arithmetic computational complexities of the Cholesky's and QR factorization of a matrix are upper bounded by 0(log2 n) steps. Also, a new parallel method
...
...