F. N. Fritsch’s research while affiliated with Lawrence Livermore National Laboratory and other places

... Monotonicity preservation is possible with the Hermite form of the bicubic interpolant (see [4]- [6]). We have extended the algorithm described in [6] to handle piecewise monotonic data (such as a typical pressure table) and included it in LEOS as the bimond option. ...

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The LEOS Interpolation Package

... The resolution of the (ρ, T ) grid is sufficiently fine to represent mixed-phase regions. Thermodynamic consistency, arising from the equality of mixed partial derivatives of the free energy [e.g., (∂P/∂T ) ρ = −(ρ 2 /m Fe )(∂S/∂ρ) T ], is assessed by using BIMOND interpolation [187] and finite-difference computations of the derivatives; we calculate that such conditions are accurately satisfied on all points with the exception of those in close proximity to phase transitions. This is to be expected, and we find that our tabular Fe EOS models are similar to other multiphase EOS tables we have recently made in this regard [136]. ...

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Wide-ranged multiphase equation of state for iron and model variations addressing uncertainties in high-pressure melting

... targets and sharp material changes) visible in both the backscatter mosaic and the video footage. By matching common landmarks in the TUC snapshots and the backscatter mosaic the position where the camera actually was during the survey is estimated for a number of occurrences, and the layback is approximated for all the mid-distances via X and Y interpolation in the time domain, using Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) (Fritsch and Carlson, 1985). Attention has been paid to finding landmarks arranged throughout the whole tow-camera survey lines, so that layback could be accurately approximated for the full dataset. ...

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Insights into seafloor litter spatiotemporal dynamics in urbanized shallow Mediterranean bays. An optimized monitoring protocol using towed underwater cameras

... The models provide wind speed data for the historical period as well as SSP predictions. In the cases that grid sizes were different, data were regridded by means of the Bicubic Interpolation method [35]. ...

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Copula-based projections of wind power: Ireland as a case study

... where ⊙ represents element-wise multiplication. Thus, AdaUp can leverage the underlying content information from input frames at different channels and utilize it to get better performance than the mainstream up-sampling operations, pixel shuffle, or interpolations (Carlson and Fritsch 1985;Schaefer, McPhail, and Warren 2006). ...

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QMambaBSR: Burst Image Super-Resolution with Query State Space Model

... In order to avoid jumps of the day-ahead contracts volatility, both functions g and h are smoothed during calibration. At each step of the fixed point algorithm, we update g and h as piece-wise constant functions and then interpolate it using the monotonicity preserving algorithm PCHIP of Fritsch and Butland (1984). Despite the smoother results, the algorithm is more time-consuming due to the numerical optimization involved in the calibration. ...

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Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration

... [76] We used the spline function in R (R Development Core Team 2019) to impute the permanent gaps in the time series of the above mentioned seven indices. The method by Fritsch and Carlson (1980) [77] was adopted to fit a piecewise monotonic cubic function for each index, which was then used to predict the missing data in the time series. ...

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Vegetation Dynamic in a Large Floodplain Wetland: The Effects of Hydroclimatic Regime

... d are found using the following equations [33]. ...

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Simplified and Smoothed Rapidly-Exploring Random Tree Algorithm for Robot Path Planning

... As the m-D data samples has different time bins, we utilize image processing methods to interpolate m-D signature, which means the transformed number of time bins is larger than motion time periods. For the interpolation method, the traditional bi-cubic interpolation is adopted to consider the effect from the neighborhood for interpolating pixel values of unknowns [14]. Finally, we transform each concatenated signature sample ...

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Activity Recognition Based on Micro-Doppler Signature with In-Home Wi-Fi

... where is incoming electron or positron energy, is the produced photon energy and ̃( , , ) is the total scaled bremsstrahlung energy-weighted cross-section from interpolation of the Seltzer and Berger [77], given in cm 2 . Note that all interpolations in this paper are done using cubic Hermite spline interpolation [78]. These cross-sections are defined for ...

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Toward Highly Accurate Multigroup Coupled Photon-Electron-Positron Cross-Sections for the Boltzmann Fokker-Planck Equation