Accuracy and stability of numerical algorithms /
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| Format: | Book |
| Language: | English |
| Published: |
Philadelphia :
Society for Industrial and Applied Mathematics,
[1996]
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| Subjects: |
Table of Contents:
- Principles of Finite Precision Computation
- Relative Error and Significant Digits
- Sources of Errors
- Precision Versus Accuracy
- Backward and Forward Errors
- Conditioning
- Cancellation
- Solving a Quadratic Equation
- Computing the Sample Variance
- Solving Linear Equations
- Accumulation of Rounding Errors
- Instability Without Cancellation
- Increasing the Precision
- Cancellation of Rounding Errors
- Rounding Errors Can Be Beneficial
- Stability of an Algorithm Depends on the Problem
- Rounding Errors Are Not Random
- Designing Stable Algorithms
- Misconceptions
- Rounding Errors in Numerical Analysis
- Floating Point Arithmetic
- Floating Point Number System
- Model of Arithmetic
- IEEE Arithmetic
- Aberrant Arithmetics
- Exact Subtraction
- Fused Multiply-Add Operation
- Choice of Base and Distribution of Numbers
- Statistical Distribution of Rounding Errors
- Alternative Number Systems
- Elementary Functions
- Accuracy Tests
- Inner and Outer Products
- The Purpose of Rounding Error Analysis
- Running Error Analysis
- Notation for Error Analysis
- Matrix Multiplication
- Complex Arithmetic
- Miscellany
- Error Analysis Demystified
- Other Approaches
- Summation
- Summation Methods
- Error Analysis
- Compensated Summation
- Other Summation Methods
- Statistical Estimates of Accuracy
- Choice of Method
- Polynomials
- Horner's Method
- Evaluating Derivatives
- The Newton Form and Polynomial Interpolation
- Matrix Polynomials
- Norms
- Vector Norms.