Monotone cubic spline interpolation for functions with a strong gradient

Aràndiga, Francesc; Baeza, Antonio; Yáñez, Dionisio F.

doi:10.1016/j.apnum.2021.11.007

Cited by 6 publications

(12 citation statements)

References 14 publications

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“…Spline interpolation has been widely used to approximate intermediate values with a polynomial [24]. In this study, rst order, second order, and third order spline interpolations were used for comparison.…”

Section: Comparison Of Methods 421 Spline Interpolationmentioning

confidence: 99%

A Missing RR Interval Complement Method Based on Respiratory Features

Nomura

Yoshida

2022

ABE

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Advanced technologies in bioinstrumentation allows easy monitoring of biometric signals such as electrocardiogram (ECG) and respiration. In order to improve unreliable monitoring due to missing RR intervals (RRIs), this paper proposes a missing RRI complement method based on respiratory features. The proposed method rst selects respiratory features from the measured data based on Granger causality, and then complements the missing RRIs based on a dynamic linear model (DLM) for RRIs with selected features. The performance of the proposed method was evaluated by comparison with standard spline interpolation, standard regression, and a vector autoregressive (VAR) model. The results are discussed in terms of the effectiveness of respiratory feature selection and utilization of the DLM to capture temporal uctuations.

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Section: Comparison Of Methods 421 Spline Interpolationmentioning

confidence: 99%

A Missing RR Interval Complement Method Based on Respiratory Features

Nomura

Yoshida

2022

ABE

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“…It is easy to get that ( 2)-( 3) corresponds to the following linear system (see more details in [2]):…”

Section: Notation Cubic Splines In Hermite Formmentioning

confidence: 99%

“…We use the same notation as in [2]. We start with the problem of piecewise cubic Hermite interpolation.…”

Section: Notation Cubic Splines In Hermite Formmentioning

confidence: 99%

“…The authors have participated in a contribution [2] where a monotonicity-preserving reconstruction is proposed using nonlinear reconstructions of the first derivatives at the interior points. During the review process of the paper one of the reviewers raised the following question: By changing the first derivative at the endpoints of the interval, is it possible to find twice continuously differentiable monotonicity preserving cubic spline interpolants?…”

Section: Introductionmentioning

confidence: 99%

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A note on some bounds between cubic spline interpolants depending on the boundary conditions: Application to a monotonicity property

Baeza

Yáñez

2022

Applied Numerical Mathematics

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“…There are many procedures in the literature for calculating these derivatives. Thus, it is worth mentioning the works of Akima [14], Catmull and Rom [15], Kobza [16], as well as recent works [17][18][19][20][21]. Quartic spline regression could also be used, as in [22], but this approach is left for a future study.…”

Section: Introductionmentioning

confidence: 99%

Spline Regression Mathematical Model for Obtaining a Sustainable Management in Young Beech (<em>Fagus sylvatica</em> L.) Stands

Crainic,

Curila,

Curila

et al. 2024

Preprint

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Having in view the sustainable management of forests, the intensity of silvotechnical interventions is analyzed and documented for young mixed beech stands regenerated naturally by taking into account the allometric relationships between some representative dendrometric elements, respectively, between the height of the trees and the corresponding diameter of their crowns. For this purpose, a functional dependence is established between the height and diameter of the tree crown from young beech stands within which silvotechnical interventions were or were not applied. A mathematical model based on cubic spline regression was developed, also taking into account the determination of the average diameter of the crown for each stand. This average diameter can be used to determine the optimal number of trees per surface unit (ha) at a given time. The research was carried out in three young beech stands, through statistical-mathematical inventories, on sample plots of 300 square meters with a tolerance of 10% and a coverage probability of 90%. The optimal diameter of the crown was obtained by applying the spline regression model, and the most appropriate functional dependence was established, resulting in a linear regression law with a positive slope.

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Monotone cubic spline interpolation for functions with a strong gradient

Cited by 6 publications

References 14 publications

A Missing RR Interval Complement Method Based on Respiratory Features

A Missing RR Interval Complement Method Based on Respiratory Features

A note on some bounds between cubic spline interpolants depending on the boundary conditions: Application to a monotonicity property

Spline Regression Mathematical Model for Obtaining a Sustainable Management in Young Beech (<em>Fagus sylvatica</em> L.) Stands

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