A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures

By H. Akima. 1970

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

1. Ian Henriksen
2. H. Gordon
3. Vika Grigorieva
4. Tuomas Laurila
5. Jukka Alm
6. Guoqiang Mao
7. Baris Fidan
8. Ke Zhang

Citations in the corpus

• The CSIRO Mk3 climate system model (2002, methodology): “The vertical interpolations in (5.5) are performed using Akima (1970) cubic interpolation.”
• Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking (2009, methodology): “Using Akima splines (see Akima (1996a), Akima (1996b) and Akima (1970)) the smoothed values obtained from the GAM are interpolated to estimate the RSS at each grid center. The synthetic model for the specific sniffer is the generated RSS-grid information with an estimated RSS for each grid point. Re”
• Monotone Piecewise Cubic Interpolation (1980, methodology): “Standard algorithms such as the three point difference formula, the "geometric mean" used by Akima [1], the least squares procedure of Ellis and McLain [6], or requiring p(x) to be a cubic spline do not guarantee monotonicity.”
• Mesoscale eddies in the northwestern subtropical Pacific Ocean: Statistical characteristics and three-dimensional structures (2013, methodology): “Potential temperature θ and salinity S data in each profile are linearly interpolated onto 101 vertical levels from the surface to 1000 dbar with an interval of 10 dbar using the Akima spline method [Akima, 1970].”
• Pelagic Sargassum in the Tropical North Atlantic (2016, methodology): “The equation for dx was solved explicitly by iteration, and Akima cubic spline (Akima 1970) was used to interpolate gridded model currents to the time and location.”
• Expectations, Bond Yields and Monetary Policy (2005, unknown): “The interpolation algorithm used by the Treasury is referred to as a “quasi-cubic Hermite splines” method, and follows a piecewise interpolation algorithm developed in Akima (1970). The inclusion of off-the-run securities that are not necessarily trading at par means that the treasury curve is not a”
• Splatter: simulation of single-cell RNA sequencing data (2017, methodology): “Splat models these kinds of changes by generating a Brownian 20 bridge (a random walk with fixed end points) between the two end cells of a path, which 21 is then smoothed and interpolated using an Akima spline [35,36].”
• SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python (2019, methodology): “…construct several common ways of interpolating data: CubicSpline (SciPy 0.18) 88 constructs a twice differentiable piecewise cubic function, Akima1DInterpolator and PCHIPInterpolator implement two classic prescriptions for constructing a C 1 continuous monotone shape-preserving interpolator 89,90 .”
• Assessment of the reliability of wave observations from voluntary observing ships: Insights from the validation of a global wind wave climatology based on voluntary observing ship data (2003, methodology): “For the spatial interpolation into unsampled locations we used the modified method of local procedures [Akima, 1970] in combination with 2-D Lanczos filtering [Lanczos, 1956; Duchon, 1979].”
• Scalar Similarity for Relaxed Eddy Accumulation Methods (2006, methodology): “First, any missing data and outliers detected were filled using an interpolation (Akima, 1970).”