Kontak, Max: Novel algorithms of greedy-type for probability density estimation as well as linear and nonlinear inverse problems. 2018
Inhalt
- Danksagung
- Zusammenfassung
- Abstract
- Contents
- Chapter 1. Introduction
- Part I. Basics
- Chapter 2. Notation and fundamentals of functional analysis
- 2.1. Spherical geometry
- 2.2. Fundamentals of functional analysis
- 2.3. Function spaces
- 2.4. Spherical harmonics
- 2.5. Zonal functions
- Chapter 3. Greedy algorithms and matching pursuits
- Part II. A greedy algorithm for density estimation
- Chapter 4. Fundamentals of probability theory and statistics
- 4.1. Basics of probability theory
- 4.2. Kernel density estimators
- 4.3. Sampling from probability distributions on the real line and the sphere
- Chapter 5. A greedy algorithm for the estimation ofprobability density functions
- Part III. Greedy algorithms for inverse problems
- Chapter 6. Theory of inverse problems
- Chapter 7. Inverse gravimetry
- Chapter 8. Regularized Functional Matching Pursuit (RFMP)
- 8.1. Problem setting
- 8.2. Functional Matching Pursuit
- 8.3. Regularized Functional Matching Pursuit
- 8.4. Properties of the algorithm and applications
- Chapter 9. Regularized Weak Functional Matching Pursuit (RWFMP)
- 9.1. Weak Functional Matching Pursuit (WFMP)
- 9.2. The Regularized Weak Functional Matching Pursuit (RWFMP)
- 9.3. Numerical Example
- Chapter 10. RFMP for nonlinear inverse problems (RFMP_NL)
- Part IV. Final remarks
- Bibliography