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9780898713626

Afternotes on Numerical Analysis

by
  • ISBN13:

    9780898713626

  • ISBN10:

    0898713625

  • Format: Paperback
  • Copyright: 1996-07-01
  • Publisher: Society for Industrial & Applied

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Summary

There are many textbooks to choose from when teaching an introductory numerical analysis course, but there is only one Afternotes on Numerical Analysis. This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner.

Table of Contents

Nonlinear Equations: Lecture
By the Dawn's Early Light
Interval Bisection
Relative Error
Lecture
Newton's Method
Reciprocals and Square Roots
Local Convergence Analysis
Slow Death
Lecture
A Quasi-Newton Method
Rates of Convergence
Iterating for a Fixed Point
Multiple Zeros
Ending with a Proposition
Lecture
The Secant Method
Convergence
Rate of Convergence
Multipoint Methods
Muller's Method
The Linear-Fractional Method
Lecture
A Hybrid Method
Errors, Accuracy, and Condition Numbers
Computer Arithmetic: Lecture
Floating-Point Numbers
Overflow and Underflow
Rounding Error
Floating-point Arithmetic
Lecture
Computing Sums
Backward Error Analysis
Perturbation Analysis
Cheap and Chippy Chopping
Lecture
Cancellation
The Quadratic Equation
That Fatal Bit of Rounding Error
Envoi
Linear Equations: Lecture
Matrices, Vectors, and Scalars
Operations with Matrices
Rank-One Matrices
Partitioned Matrices
Lecture
Theory of Linear Systems
Computational Generalities
Triangular Systems
Operation Counts
Lecture
Memory Considerations
Row Oriented Algorithms
A Column Oriented Algorithm
General Observations on Row and Column Orientation
Basic Linear Algebra Subprograms
Lecture
Positive Definite Matrices
The Cholesky Decomposition
Economics
Lecture
Inner-Product Form of the Cholesky Algorithm
Gaussian Elimination
Lecture
Pivoting
BLAS
Upper Hessenberg and Tridiagonal Systems
Lecture
Vector Norms
Matrix Norms
Relative Error
Sensitivity of Linear Systems
Lecture
The Condition of Linear Systems
Artificial Ill Conditioning
Rounding Error and Gaussian Elimination
Comments on the Analysis
Lecture
The Wonderful Residual: A Project
Introduction
More on Norms
The Wonderful Residual
Matrices with Known Condition
Invert and Multiply
Cramer's Rule
Submission
Polynomial Interpolation: Lecture
Table of Contents provided by Publisher. All Rights Reserved.

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