LU 분해

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  1. """Performs an LU Decomposition of A (which must be square) into PA = LU.[1]
  2. LU Decomposition Structure to access L, U and piv.[2]
  3. For generic square matrices, the backslash operator computes the solution of the linear system using LU decomposition.[3]
  4. To recreate the answer computed by backslash, compute the LU decomposition of A .[3]
  5. LU decomposition method, based on the Gaussian elimination, is particularly well suited for spars and large-scale problems.[4]
  6. The main contribution of this paper is in utlizing this solution to implement LU decomposition technique on the basic DEA models which is more accurate and numerically stable.[4]
  7. The major steps required to solve an equation system by LU decomposition are as follows.[5]
  8. We now illustrate the LU decomposition process by solving (2.10) with p = 1 .[5]
  9. LU decomposition can be viewed as the matrix form of Gaussian elimination.[6]
  10. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.[6]
  11. Therefore, to find the unique LU decomposition, it is necessary to put some restriction on L and U matrices.[6]
  12. Computing an LU decomposition using this algorithm requires 2 3 n 3 {\displaystyle {\tfrac {2}{3}}n^{3}} floating-point operations, ignoring lower-order terms.[6]
  13. The bookkeeping exercise really did give us an LU decomposition.[7]
  14. ’s scheme, we propose a novel bilateral authentication scheme with user anonymity using LU decomposition of matrices.[8]
  15. From the matrix theory, LU decomposition factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix.[8]
  16. Let be a square matrix; an LU decomposition of matrix is the form , where is a lower triangular matrix and is an upper triangular matrix.[8]
  17. We can introduce the LU decomposition into the user authentication system to ensure the security of the system.[8]
  18. This function performs an LU decomposition of the given square matrix argument the results are returned in a list of named components.[9]
  19. Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix.[10]
  20. Code that performs LU decomposition is shown below.[11]
  21. This app performs LU decomposition of a square matrix and will solve a set of linear inhomogeneous equations.[11]
  22. When f is changed the last steps can be done without recomputing the LU decomposition.[12]
  23. Solution algorithms are most efficient if these patterns are taken into account in the LU decomposition.[12]
  24. The LU decomposition may not exist for a matrix .[13]
  25. If the LU decomposition exists then it is unique.[13]
  26. The LU decomposition provides an efficient means of solving linear equations.[13]
  27. The reason that has all diagonal entries set to 1 is that this means the LU decomposition is unique.[13]
  28. The principles of LU decomposition are described in most numerical methods texts.[14]
  29. These compact schemes are meant to perform all operations in-place so that the matrix A is overwritten by the desired LU decomposition.[14]
  30. rarely discuss the various LU decomposition options such as Crout, Doolittle and Cholesky A single-file code that implements and tests these methods can be downloaded here.[14]
  31. Today we are going to do an LU decomposition problem.[15]
  32. Now, what do you have to remember when doing an LU decomposition problem?[15]
  33. But we're not just doing elimination, we're finding an LU decomposition.[15]
  34. You can't find an LU decomposition if you have to do a row exchange in elimination.[15]
  35. The system to be solved is, and the solution is found using LU decomposition of the matrix .[16]

소스

  1. ↑ LU Decomposition in Python and NumPy
  2. ↑ LUDecomposition
  3. ↑ 3.0 3.1 LU matrix factorization
  4. ↑ 4.0 4.1 LU Decomposition in DEA with an Application to Hospitals
  5. ↑ 5.0 5.1 LU Decomposition - an overview
  6. ↑ 6.0 6.1 6.2 6.3 LU decomposition
  7. ↑ Gauss Elimination and LU Decomposition
  8. ↑ 8.0 8.1 8.2 8.3 Applying LU Decomposition of Matrices to Design Anonymity Bilateral Remote User Authentication Scheme
  9. ↑ lu.decomposition function
  10. ↑ MATHEMATICA TUTORIAL, Part 2.2: LU
  11. ↑ 11.0 11.1 LU decomposition
  12. ↑ 12.0 12.1 LU Decomposition
  13. ↑ 13.0 13.1 13.2 13.3 LU Decomposition for Solving Linear Equations
  14. ↑ 14.0 14.1 14.2 Decomposition schemes of Crout, Doolittle and Cholesky
  15. ↑ 15.0 15.1 15.2 15.3 Unit I: Ax = b and the Four Subspaces
  16. ↑ Linear Algebra — GSL 2.6 documentation

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