Author | Branham, Richard L. author |
---|---|
Title | Scientific Data Analysis [electronic resource] : An Introduction to Overdetermined Systems / by Richard L. Branham |
Imprint | New York, NY : Springer New York, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3362-6 |
Descript | X, 237 p. online resource |
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