Accuracy and stability of numerical algorithms

@inproceedings{Higham1991AccuracyAS,
  title={Accuracy and stability of numerical algorithms},
  author={N. Higham},
  year={1991}
}
  • N. Higham
  • Published 1991
  • Computer Science, Mathematics
From the Publisher: What is the most accurate way to sum floating point numbers? What are the advantages of IEEE arithmetic? How accurate is Gaussian elimination and what were the key breakthroughs in the development of error analysis for the method? The answers to these and many related questions are included here. This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory… Expand
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References

SHOWING 1-10 OF 14 REFERENCES
A note on complex division
  • 31
Rounding errors in algebraic processes
  • 1,122
10 Proof of Wedin's
  • The Equality Constrained Least Squares Problem . . . . . . . . . 396 20.9.1 Perturbation Theory . . . . . . . . . . . . . . . . . . . . . 396 20.9.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 20
303 16 The Sylvester Equation 305 16.1 Solving the
  • 1 How to Estimate Componentwise Condition Numbers . . . . . . . 288 15.2 The p-Norm Power Method . . . . . . . . . . . . . . . . . . . . . . 289 15 301 15.7.1 LAPACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Problems
333 17.5 Stopping an Iterative Method . . . . . . . . . . . . . . . . . . . . 335 17 337 xii Contents 18 Matrix Powers 339 18.1 Matrix Powers in Exact Arithmetic
  • 333 17.5 Stopping an Iterative Method . . . . . . . . . . . . . . . . . . . . 335 17 337 xii Contents 18 Matrix Powers 339 18.1 Matrix Powers in Exact Arithmetic
416 22.2 Primal and Dual Systems 424 22.3.2 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 22.3.3 Dealing with Instability . . . . . . . . . . . . . . . . . . . . 426 22
  • 416 22.2 Primal and Dual Systems 424 22.3.2 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 22.3.3 Dealing with Instability . . . . . . . . . . . . . . . . . . . . 426 22
Aggregated Householder Transformations
  • Aggregated Householder Transformations
B Acquiring Software
  • B Acquiring Software
C.1 Basic Linear Algebra Subprograms
  • C.1 Basic Linear Algebra Subprograms
Circulant Linear Systems . . . . . . . . . . . . . . . . . . . . . . . 454 24.3 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 456 Problems
  • Circulant Linear Systems . . . . . . . . . . . . . . . . . . . . . . . 454 24.3 Notes and References . . . . . . . . . . . . . . . . . . . . . . . . . 456 Problems
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