The Dual Reciprocity Boundary Element Method for One-Dimensional Nonlinear Parabolic Partial Differential Equations

Alipour, Peyman

doi:10.1007/s10958-023-06642-4

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2024

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“…At the same time, for medium-and large-scale problems, in order to reduce the storage requirements and accelerate the speed of GSVD, the randomized GSVD method [15,16] is used, and then we obtain the randomized GTRTLS (RGTRTLS) algorithm. For the randomized algorithms of large-scale matrix decompositions and their application to ill-conditioned problems, one can see [17][18][19][20] for examples and details.…”

Section: Introductionmentioning

confidence: 99%

Regularization Total Least Squares and Randomized Algorithms

Yang,

Liu,

2024

Mathematics

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In order to achieve an effective approximation solution for solving discrete ill-conditioned problems, Golub, Hansen, and O’Leary used Tikhonov regularization and the total least squares (TRTLS) method, where the bidiagonal technique is considered to deal with computational aspects. In this paper, the generalized singular value decomposition (GSVD) technique is used for computational aspects, and then Tikhonov regularized total least squares based on the generalized singular value decomposition (GTRTLS) algorithm is proposed, whose time complexity is better than TRTLS. For medium- and large-scale problems, the randomized GSVD method is adopted to establish the randomized GTRTLS (RGTRTLS) algorithm, which reduced the storage requirement, and accelerated the convergence speed of the GTRTLS algorithm.

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