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Scientific Data Analysis An Introduction to Overdetermined Systems

This monograph is concerned with overdetermined systems, inconsistent systems with more equations than unknowns, in scientific data reduction. It is not a text on statistics, numerical methods, or matrix cOmputations, although elements of all three, especially the latter, enter into the discussion....

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Bibliographic Details
Main Author: Branham, Richard L. Jr
Format: eBook
Language:English
Published: New York, NY Springer New York 1990, 1990
Edition:1st ed. 1990
Subjects:
Artificial Intelligence / Data Processing
Probability Theory
Probabilities
Data Science
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Properties of Floating-Point Numbers
  • 1.1. Introduction
  • 1.2. Representation of Floating-Point Numbers
  • 1.3. Characteristics of Floating-Point Numbers
  • 1.4. Violation of the Laws of Arithmetic
  • 1.5. Accurate Floating-Point Summation
  • 2 Matrices, Norms, and Condition Numbers
  • 2.1. Matrices
  • 2.2. Vector and Matrix Norms
  • 2.3. The Condition Number
  • 3 Sparse Matrices
  • 3.1. Introduction
  • 3.2. Sparse Techniques for Null Elements Following a Pattern
  • 3.3. Sparse Techniques with Null Elements in Random Locations
  • 3.3.1. The Bit Map
  • 3.3.2. Paired Vectors
  • 3.3.3. The Linked List
  • 3.3.4. Hashing
  • 3.4. Conclusions
  • 4 Introduction to Overdetermined Systems
  • 4.1. Introduction
  • 4.2. Mathematical Theory of Overdetermined Systems
  • 4.3. Modeling Errors and Outliers
  • 4.4. Solution of Linear Systems
  • 5 Linear Least Squares
  • 5.1. The Normal Equations
  • 5.2. Solution of the Normal Equations
  • 5.3. The Variance-Covariance and Correlation Matrices
  • 5.4. Orthogonal Transformations
  • 5.5. Iteratively Reweighted Least Squares
  • 5.6. Constrained Least Squares
  • 6 The L1 Method
  • 6.1. Introduction
  • 6.2. General Considerations of the Li Solution
  • 6.3. Linear Programming
  • 6.4. The L1 Algorithm and Error Estimates
  • 7 Nonlinear Methods
  • 7.1. Introduction
  • 7.2. Gradient Methods
  • 7.3. Nongradient Methods
  • 8 The Singular Value Decomposition
  • 8.1. Introduction
  • 8.2. Calculating the SVD
  • 8.3. Total Least Squares
  • 8.4. Singular Value Analysis

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