The Fast Gauss Transform

By Leslie Greengard, J. Strain. 1991

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Citations in the corpus

Prototypal Analysis and Prototypal Regression (2017, methodology): “For the Gaussian kernel, the time complexity for the inner product can be reduced to O(n1 + n2) via the fast Gauss transform (Greengard and Strain, 1991) or improved fast Gauss transform (Yang et al.”
Efficient mean-shift tracking via a new similarity measure (2005, methodology): “If the Gaussian kernel is used, we can apply the fast Gauss transform [18] to the tracking algorithm to reduce its computational complexity from quadratic order to linear order, as was done in .”
Robust numerical methods for contingent claims under jump diffusion processes (2005, methodology): “Our next two numerical tests incorporate the use of an automatic timestep size selector as described in Johnson (1987). It is not generally possible to achieve second order convergence for American options using constant timesteps (Forsyth and Vetzal, 2002).”
Fast Direct Methods for Gaussian Processes (2014, methodology): “In general, however, it is difficult to obtain accurate values for the determinant in a robust and reliable manner.”
Background and foreground modeling using nonparametric kernel density estimation for visual surveillance (2002, methodology): “Since color spaces are low in dimensionality, efficient computation of kernel density estimation for color pdfs can be achieved using the Fast Gauss Transform algorithm [34], [35].”
Fast large scale Gaussian process regression using approximate matrix-vector products (2006, methodology): “The fast Gauss transform (FGT) is a special case where FMM ideas were used for the Gaussian potential [6].”
Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow (2007, methodology): “At this moment, the diffusion is terminated and the kernel density estimate is re-estimated by mean of, e.g., the fast Gauss transform [51].”
Solving elliptic problems with non-Gaussian spatially-dependent random coefficients (2009, methodology): “However, we note that ~ qi is nothing more but a sum of a series of Gaussian functions, which implies that the fast Gauss transform (FGT) [34,19] can be employed to accelerate the calculation.”
A robust algorithm for point set registration using mixture of Gaussians (2005, methodology): “In this case, a fast numerical scheme, like the fast Gauss Transform [16] , can be used to overcome this obstacle.”
The design and analysis of information processing systems ] From Linear Adaptive Filtering to Nonlinear Information Processing (2009, methodology): “In probability IEEE SIGNAL PROCESSING MAGAZINE [17] NOVEMBER 2006 spaces, the role of optimization is therefore to minimize the KLD between these two distributions: min w It can be shown that if we write z = f (x) + e, where e is the error and f (x) is the mapping function, minimizing the KLD is equ”
On the Numerical Evaluation of Option Prices in Jump Diffusion Processes (2007, methodology): “We note that the Fast Gauss Transform (Greengard and Strain, 1991 ) has been suggested as a rapid method of evaluating correlation integrals in the Merton and Kou models.”
Fast High-dimensional Kernel Summations Using the Monte Carlo Multipole Method (2008, methodology): “As a result, many previous methods [7] have focused on bounding the absolute error.”
Fast geometric learning with symbolic matrices (2020, unknown): “Multiscale schemes can be used to handle singular kernels [7, 8, 50, 52, 115] or compress generic operators [5, 17, 55].”