숄레스키 분해

수학노트
Pythagoras0 (토론 | 기여)님의 2021년 2월 17일 (수) 00:53 판
(차이) ← 이전 판 | 최신판 (차이) | 다음 판 → (차이)
둘러보기로 가기 검색하러 가기

노트

위키데이터

말뭉치

  1. Cholesky decomposition, also known as Cholesky factorization, is a method of decomposing a positive-definite matrix.[1]
  2. Cholesky decomposition and other decomposition methods are important as it is not often feasible to perform matrix computations explicitly.[1]
  3. The function chol() performs Cholesky decomposition on a positive-definite matrix.[1]
  4. Cholesky decomposition is frequently utilized when direct computation of a matrix is not optimal.[1]
  5. The algorithms for such a problem are commonly known as the modified Cholesky decomposition.[2]
  6. ---the calculation of E should be a small multiple of n 2 operations in the overall Cholesky decomposition of n 3 3 operations.[2]
  7. If A 11 > 0 , we tentatively take a Cholesky decomposition step.[2]
  8. If algo='SCHNABEL2' is set in the input, the code will not try the tentative Cholesky decomposition with E j = 0 at the beginning.[2]
  9. For this reason, the LDL decomposition is often called the square-root-free Cholesky decomposition.[3]
  10. For linear systems that can be put into symmetric form, the Cholesky decomposition (or its LDL variant) is the method of choice, for superior efficiency and numerical stability.[3]
  11. The Cholesky decomposition is commonly used in the Monte Carlo method for simulating systems with multiple correlated variables.[3]
  12. Unscented Kalman filters commonly use the Cholesky decomposition to choose a set of so-called sigma points.[3]
  13. -- Return the lower triangular matrix of a Cholesky decomposition.[4]
  14. program performs the Cholesky decomposition on a square matrix.[4]
  15. This function returns the lower Cholesky decomposition of a square matrix fed to it.[4]
  16. Because of numerical stability and superior efficiency in comparison with other methods, Cholesky decomposition is widely used in numerical methods for solving symmetric linear systems.[5]
  17. Cholesky decomposition assumes that the matrix being decomposed is Hermitian and positive-definite.[6]
  18. """Performs a Cholesky decomposition of A, which must be a symmetric and positive definite matrix.[6]
  19. Return the Cholesky decomposition, L * L.H, of the square matrix a, where L is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if a is real-valued).[7]
  20. Cholesky decomposition reduces a symmetric matrix into a lower-triangular matrix which when multiplied by it’s transpose produces the original symmetric matrix.[8]
  21. Now the cool part: using Cholesky decomposition we can solve systems of equations of any size in 2 steps.[8]
  22. Hence, has the Cholesky decomposition Let us now prove the "only if" part, starting from the hypothesis that has a Cholesky decomposition, as in the previous equation.[9]
  23. Such a decomposition is called a Cholesky decomposition.[10]
  24. The Cholesky decomposition algorithm was first proposed by Andre-Louis Cholesky (October 15, 1875 - August 31, 1918) at the end of the First World War shortly before he was killed in battle.[11]
  25. Originally, the Cholesky decomposition was used only for dense real symmetric positive definite matrices.[11]
  26. In the case of sparse matrices, the Cholesky decomposition is also widely used as the main stage of a direct method for solving linear systems.[11]
  27. Various versions of the Cholesky decomposition are successfully used in iterative methods to construct preconditioners for sparse symmetric positive definite matrices.[11]
  28. Using the generalized interval arithmetic we give a generalized cholesky decomposition.[12]
  29. I have added the Cholesky decomposition.[13]
  30. The disadvantage is, the Cholesky decomposition works only for symmetric positive definite matrices.[13]
  31. However, if A is symmetric and positive definite, we can choose the factors such that U is the transpose of L, and this is called the Cholesky decomposition.[14]
  32. I have a covariance matrix, S , which I use Cholesky decomposition to find A .[15]
  33. For this purpose, we use a linear transformation which is obtained from the Cholesky decomposition of covariance matrix and eliminate linear correlation among financial assets.[16]
  34. Cholesky decomposition can be applied for the matrixes which are positive definite and symmetric.[16]
  35. Solving linear systems is one of the principal applications of the Cholesky decomposition.[16]
  36. In this paper, we, at first, present a linear transformation based on Cholesky decomposition.[16]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Cholesky Decomposition with R Example
  2. ↑ 2.0 2.1 2.2 2.3 Cholesky Decomposition - an overview
  3. ↑ 3.0 3.1 3.2 3.3 Cholesky decomposition
  4. ↑ 4.0 4.1 4.2 Cholesky decomposition
  5. ↑ Cholesky Decomposition
  6. ↑ 6.0 6.1 Cholesky Decomposition in Python and NumPy
  7. ↑ numpy.linalg.cholesky — NumPy v1.19 Manual
  8. ↑ 8.0 8.1 Behind The Models: Cholesky Decomposition
  9. ↑ Cholesky decomposition
  10. ↑ Department of Electrical and Computer Engineering
  11. ↑ 11.0 11.1 11.2 11.3 Cholesky decomposition
  12. ↑ A Generalized Cholesky Decomposition for Interval Matrix
  13. ↑ 13.0 13.1 Cholesky decomposition in PHP
  14. ↑ CholeskyDecomposition Class
  15. ↑ Why does the resulting matrix from Cholesky decomposition of a covariance matrix when multiplied by its transpose not give back the covariance matrix?
  16. ↑ 16.0 16.1 16.2 16.3 Usage of Cholesky Decomposition in order to Decrease the Nonlinear Complexities of Some Nonlinear and Diversification Models and Present a Model in Framework of Mean-Semivariance for Portfolio Perform

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'cholesky'}, {'LEMMA': 'decomposition'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=숄레스키_분해&oldid=51138"