Journal ArticleDOI
Monotone Piecewise Cubic Interpolation
F. N. Fritsch,R. E. Carlson +1 more
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In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.Abstract:
In a 1980 paper [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone $\mathcal{C}^1 $ piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm.read more
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SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
Pauli Virtanen,Ralf Gommers,Travis E. Oliphant,Matt Haberland,Matt Haberland,Tyler Reddy,David Cournapeau,Evgeni Burovski,Pearu Peterson,Warren Weckesser,Jonathan Bright,Stefan van der Walt,Matthew Brett,Joshua Wilson,K. Jarrod Millman,Nikolay Mayorov,Andrew Nelson,Eric Jones,Robert Kern,Eric B. Larson,CJ Carey,Ilhan Polat,Yu Feng,Eric Moore,Jake Vanderplas,Denis Laxalde,Josef Perktold,Robert Cimrman,Ian Henriksen,Ian Henriksen,E. A. Quintero,Charles R. Harris,Anne M. Archibald,Antônio H. Ribeiro,Fabian Pedregosa,Paul van Mulbregt,SciPy . Contributors +36 more
TL;DR: SciPy as discussed by the authors is an open source scientific computing library for the Python programming language, which includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics.
Journal ArticleDOI
SciPy 1.0: fundamental algorithms for scientific computing in Python.
Pauli Virtanen,Ralf Gommers,Travis E. Oliphant,Matt Haberland,Matt Haberland,Tyler Reddy,David Cournapeau,Evgeni Burovski,Pearu Peterson,Warren Weckesser,Jonathan Bright,Stefan van der Walt,Matthew Brett,Joshua Wilson,K. Jarrod Millman,Nikolay Mayorov,Andrew Nelson,Eric Jones,Robert Kern,Eric B. Larson,CJ Carey,Ilhan Polat,Yu Feng,Eric Moore,Jake Vanderplas,Denis Laxalde,Josef Perktold,Robert Cimrman,Ian Henriksen,Ian Henriksen,E. A. Quintero,Charles R. Harris,Anne M. Archibald,Antônio H. Ribeiro,Fabian Pedregosa,Paul van Mulbregt,SciPy . Contributors +36 more
TL;DR: SciPy as discussed by the authors is an open-source scientific computing library for the Python programming language, which has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year.
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Journal ArticleDOI
Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
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A new procedure for gridding elevation and stream line data with automatic removal of spurious pits
TL;DR: In this article, a morphological approach to the interpolation of regular grid digital elevation models (DEMs) from surface specific elevation data points and selected stream lines is described, which has given rise to a computationally efficient interpolation procedure which couples the minimization of a terrain specific roughness penalty with an automatic drainage enforcement algorithm.
References
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Book
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TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
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