ABSTRACT
Numerical Methods for Linear Systems 50 Vector and Matrix Norms, Error Analysis, Efficiency, and Stability
Ralph Byers and Biswa Nath Datta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50-1
51 Matrix Factorizations and Direct Solution of Linear Systems Christopher Beattie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51-1
52 Least Squares Solution of Linear Systems Per Christian Hansen and Hans Bruun Nielsen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52-1
53 Sparse Matrix Methods Esmond G. Ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53-1
54 Iterative Solution Methods for Linear Systems Anne Greenbaum . . . . 54-1
Numerical Methods for Eigenvalues 55 Symmetric Matrix Eigenvalue Techniques Ivan Slapnicˇar . . . . . . . . . . . . . 55-1
56 Unsymmetric Matrix Eigenvalue Techniques David S. Watkins . . . . . . . 56-1
57 The Implicitly Restarted Arnoldi Method D. C. Sorensen . . . . . . . . . . . . 57-1
58 Computation of the Singular Value Decomposition Alan Kaylor Cline and Inderjit S. Dhillon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58-1
59 Computing Eigenvalues and Singular Values to High Relative Accuracy Zlatko Drmacˇ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59-1
60 Nonlinear Eigenvalue Problems Heinrich Voss . . . . . . . . . . . . . . . . . . . . . . . . . . 60-1
Topics in Numerical Linear Algebra 61 Fast Matrix Multiplication Dario A. Bini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61-1
62 Fast Algorithms for Structured Matrix Computations Michael Stewart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62-1
63 Structured Eigenvalue Problems — Structure-Preserving Algorithms, Structured Error Analysis Heike Faßbender . . . . . . . . . . . . . . 63-1
64 Large-Scale Matrix Computations Roland W. Freund . . . . . . . . . . . . . . . . . . 64-1
50 Vector and Matrix Norms, Error Analysis, Efficiency, and Stability Ralph Byers and Biswa Nath Datta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50-1
51 Matrix Factorizations and Direct Solution of Linear Systems Christopher Beattie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51-1
52 Least Squares Solution of Linear Systems Per Christian Hansen and Hans Bruun Nielsen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52-1
53 Sparse Matrix Methods Esmond G. Ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53-1
54 Iterative Solution Methods for Linear Systems Anne Greenbaum . . . . 54-1
Biswa Nath Datta Northern Illinois University
Calculations are subject to errors. There may be modeling errors, measurement errors, manufacturing errors, noise, equipment is subject to wear and damage, etc. In preparation for computation, data must often be perturbed by rounding it to fit a particular finite precision, floating-point format. Further errors may be introduced during a computation by using finite precision arithmetic and by truncating an infinite process down to a finite number of steps.
