Scientific Data Analysis: An Introduction to Overdetermined Systems - Rilegato

Branham, Richard L. Jr.

Rilegato

ISBN 10: 0387972013 ISBN 13: 9780387972015

Casa editrice: SPRINGER NATURE, 1990

Riassunto

This monograph considers overdetermined systems, i. e. , inconsistent systems with more equations than unknowns, in scientific data reduction. Although not a text on statistics, numerical methods, or matrix computations, all three enter into the discussion. The book is intended for the scientist or engineer who has gathered data that needs to be modelled by a mathematical system, perhaps linear or non-linear, and to be solved to obtain best estimates of various parameters. Programs and subroutines, mostly in FORTRAN, a few in BASIC, and one in C, illustrate many of the techniques presented.

Su questo libro

Contenuti

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.

Product Description

Book by Branham Richard L Jr

Dettagli dell'edizione

• Editore: SPRINGER NATURE
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 0387972013
• ISBN 13: 9780387972015
• Rilegatura: Copertina rigida
• Numero di pagine: 237
• Contatto del produttore: Elevation; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; 22391; Germania