Topic
Triangular decomposition
About: Triangular decomposition is a research topic. Over the lifetime, 184 publications have been published within this topic receiving 3493 citations.
Papers published on a yearly basis
Papers
TL;DR: This work uses Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system, and gives some pure geometric criteria for the number of real physical solutions.
Abstract: We use two approaches to solve the perspective-three-point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.
1,104 citations
TL;DR: This paper reviews the turning band method and fast Fourier transform method of producing a nonconditional simulation of a multinormal random function with a given covariance structure and shows that they are formally equivalent.
Abstract: This paper reviews the turning band method and fast Fourier transform method of producing a nonconditional simulation of a multinormal random function with a given covariance structure. A review of the two common methods of conditioning the simulation to honor the data shows that they are formally equivalent. Another method for directly pondering a conditional simulation based on the LU triangular decomposition of the covariance matrix is presented. Computational and implementation difficulties are discussed.
369 citations
TL;DR: The main result is that four different existing notions of good triangular sets are equivalent, and the relationship between these notions is studied.
322 citations
TL;DR: In this article, two closely related numerical methods for the solution of eigenvalue problems called "stabilized iteration" and "mutually stabilized biiteration" are described.
Abstract: We have described two closely related numerical methods for the solution of eigenvalue problems called ‘stabilized iteration’ and ‘mutually stabilized biiteration’. The iteration process shows numerical stability, has no loss of leading figures and is self-correcting, givingsome eigenvectors immediately in the second case, in triangular decomposition in an important special case of the stabilized iteration, called ‘Treppeniteration’. The processes are mathematically closely related toRutishauser's
LR-Transformation, but differ in numerical aspect. A certain mixed process, based onRutishauser and the author's ideas, seems to be the optimum way with regard to both security and numerical labor.
137 citations
TL;DR: An overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory and new techniques that are essential to the recent success and for future research directions in the development of triangular decomposition methods.
87 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 7 |
| 2020 | 9 |
| 2019 | 5 |
| 2018 | 9 |
| 2017 | 8 |