Table of contents
Backward Error Analysis and Numerical Software
Plan of Talk
Stability
Example - Sample Variance
Error Analysis
Example
Example (cont’d)
Diapositive PPT
Example (cont’d)
Example (cont’d)
Example (cont’d)
Example (cont’d)
Componentwise and Normwise
Condition
Example
Diapositive PPT
Condition Number for Linear Equations
Condition and Error Analysis
Example
Backward Error as Perturbations in the Data
Backward Error as … (cont’d)
Example
Backward Error Analysis
Backward Error and Perturbation Analysis
The Purpose of Error Analysis
Diapositive PPT
LAPACK and Error Bounds
The BLAS, LAPACK and ScaLAPACK
The Three Levels of BLAS
Why Higher Level BLAS?
BLAS for Performance
Publication of the Specifications of the BLAS
LAPACK
Benefits of LAPACK
Diapositive PPT
Diapositive PPT
Diapositive PPT
Performance Improvements
Error Bounds in LAPACK
Error Bounds in LAPACK: Example 1
Error Bounds in LAPACK: Example 2
Error Bounds in LAPACK: Example 2 (cont’d)
Error Bounds in LAPACK: Example 2 (cont’d)
Diapositive PPT
LAPACK - Summary
ScaLAPACK
Diapositive PPT
ScaLAPACK Structure
ScaLAPACK Summary
Hierarchy of Building Blocks
Developments Since Wilkinson
Diagonal Matrix Example
Backward Errors in Other Areas
What to do if Software does not Provide Estimates?
PRECISE
Quality of Reliable Software
References
Closing Remarks
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