A comparative analysis of local cubic splines

Жанлав, Т.; Mijiddorj, Renchin-Ochir

doi:10.1007/s40314-018-0651-1

Cited by 7 publications

(8 citation statements)

References 3 publications

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“…The super-convergence properties of S 5 (x) and S 5 (x) of the integro quintic spline are given by Theorem 3.4 in [23] as well as those S 3 (x) of the integro cubic spline [21]. CONJECTURE 3.2.…”

Section: General Algorithm For Local Integro Splinesmentioning

confidence: 98%

Algorithm to Construct Integro Splines

Mijiddorj

Жанлав

2021

ANZIAM J.

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We study some properties of integro splines. Using these properties, we design an algorithm to construct splines $S_{m+1}(x)$ of neighbouring degrees to the given spline $S_m(x)$ with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.

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Section: General Algorithm For Local Integro Splinesmentioning

confidence: 98%

Algorithm to Construct Integro Splines

Mijiddorj

Жанлав

2021

ANZIAM J.

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“…However, there are some restrictions that the polynomials, their first-order and second-order derivatives are all continuous at the knots to generate a smooth curve (Lavery, 2002(Lavery, , 2000Zhanlav and Mijiddorj, 2018). Moreover, due to the unstable polynomial functions and the fewer measured points, over-fitting often occurs in the boundary region.…”

Section: Curve-fitting Functionsmentioning

confidence: 99%

Technical note: Improving the Initial Conditions of Hydrological Model with Reanalysis Soil Moisture Data

Liu

Ao²,

Zhou³

2022

Preprint

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Abstract. The initial conditions (e.g., soil moisture content) of the hydrological model, which is usually obtained from the warm-up of the hydrological modeling, significantly impact the simulation efficiency. However, spending the valuable data in warm-up instead of calibration and validation is luxurious. In order to improve hydrological simulation efficiency in the case of no warm-up phase, this paper proposes a methodology to fill the gap via improving the initial conditions of the hydrological model using an alternative global soil moisture dataset. Specifically, three soil moisture (SM) variables of the initial conditions from the Block-wise use of the TOPMODEL (BTOP) model and ERA5-Land reanalysis data were adopted and conducted correlation analysis. Several traditional curve-fitting functions and the state-of-art technical, long-short term memory (LSTM), were applied to develop the relationship between BTOP and ERA5-Land SM variables in the Fuji and Shinano River Basin, Japan. Furthermore, four configured hydrological simulations evaluated the benefits of the proposed methodology for improving the initial conditions. As a result, LSTM outperforms the traditional curve-fitting method in constructing the relationship between variables in time and space. Moreover, the hydrological simulation cases using the initial conditions related to the SM from the ERA5-land performs better than the case without the warm-up phase, and the simulated discharge process approaches the "optimal" case with the warm-up phase. It is confirmed that the proposed methodology helps improve the initial conditions of the hydrological model using reanalysis soil moisture data.

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“…Approximating y = y(x) and its derivatives by using the integral values (1) is called integroapproximation. Splines have been widely used for this problem, see the works of Behforooz [1,2], Zhanlav [3][4][5], Mijiddorj [6,7], Lang [8][9][10], Xu [11,12], Haghighi [13,14], and Wu [15][16][17]. Generally, the obtained integro-splines have good approximation abilities.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, the convergence orders of these two approximations at the knots are all one order higher than the ordinary cases of a quartic spline. Furthermore, it was also proved in [8] that the super convergence (7) still hold even if the exact boundary function values y(x 0 ), y(x 1 ), y(x n−1 ), y(x n ) in ( 3), (4), (5) and (6) are replaced respectively by the following approximate boundary function values…”

Section: Introductionmentioning

confidence: 99%

Some new super convergence of a quartic integro-spline at the mid-knots of a uniform partition

Lang¹,

Xu²

2022

ScienceAsia

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In this paper, we study some new super convergence of a quartic integro-spline at the mid-knots of a uniform partition. We prove that the quartic integro-spline has super convergence in function values approximation (sixth order convergence), in second-order derivatives approximation (fourth order convergence) and in fourth-order derivatives approximation (second order convergence) at the mid-knots, no matter that the quartic integro-spline is determined by using four exact boundary conditions or is determined by using four approximate boundary conditions. These new super convergence properties also have been numerically examined.

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A comparative analysis of local cubic splines

Cited by 7 publications

References 3 publications

Algorithm to Construct Integro Splines

Algorithm to Construct Integro Splines

Technical note: Improving the Initial Conditions of Hydrological Model with Reanalysis Soil Moisture Data

Some new super convergence of a quartic integro-spline at the mid-knots of a uniform partition

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