Numerical recipes: the art of scientific computing, 3rd Edition

By W. Press, Saul A. Teukolsky, W. Vetterling, B. Flannery. 2007

1,178 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f8f492605119d133af9182a6af1f537d74b49205

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Citations in the corpus

A ph mesh refinement method for optimal control (2015, methodology): “The h version of the method of this paper is similar to an adaptive step-size fixed-order integration method, such as an adaptive step-size Runge– Kutta method, in the following respect: In both cases, the mesh is refined, often by step-halving or step-doubling [37], when the specified error toleran”
Eight New Millisecond Pulsars in NGC 6440 and NGC 6441 (2007, methodology): “First, all the timing parameters of NGC 6440Bwere estimated using aMonteCarlo bootstrap algorithm (Efron&Tibshirani 1993; Press et al. 1992) with a total of 1024 fake TOA data sets that are consistent with the real data set.”
pLogo: a probabilistic approach to visualizing sequence motifs (2013, methodology): “Binomial-distribution calculations were implemented according to the Incomplete Beta Function method as described previously 18 .”
Fluorophore localization algorithms for super-resolution microscopy (2014, background): “…can calculate the inverse of the Fisher information (roughly, the second derivative of the log likelihood) 34–36 and average it over all possible data sets (images) consistent with the model, which gives a prediction for the variance of 60 helps with fast convergence, but it is only a partial fix.”
A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model (2011, methodology): “The ﬁrst order condition leads to the matrix equation which is solved in a standard way using the LU decomposition algorithm [14].”
Estimating Black Carbon Aging Time-Scales with a Particle-Resolved Aerosol Model (2009, methodology): “…aerosol model to the de-121 terministic MOSAIC gas- and aerosol-chemistry code (Zaveri et al., 2008)122 in a time- or operator-splitting fashion (Press et al., 2007, Section 20.3.3).123 MOSAIC treats all the globally important aerosol species including sulfate,124 nitrate, chloride, carbonate,…”
Computation of Hypergeometric Functions (2009, methodology): “, d14 and θ stated in [57], the authors note that the error | 14| is less than 10−15 for real z and almost as small for complex z.”
Theta-Gamma-Modulated Synaptic Currents in Hippocampal Granule Cells In Vivo Define a Mechanism for Network Oscillations (2014, methodology): “Shuffling was performed by randomizing the temporal order of the LFP data points, using the linear congruential random number generator ran2 (Press et al., 2007).”
The SXS collaboration catalog of binary black hole simulations (2019, methodology): “Timestepping is done via the method of lines using a fifth-order Dormand–Prince integrator with a proportional-integral adaptive timestepping control system that chooses an appropriate step size while achieving a desired time-stepping error [145].”
The Vertical Structure of Warm Ionised Gas in the Milky Way (2008, methodology): “We have fit the 51 measurements in Figure 1 to Equation (6) using a Levenberg-Marquardt algorithm (Press et al. 1992) (the two upper limits from the Magellanic Clouds are excluded from the fit, but are used as independent tests on the validity of any fitted model).”
Efficient Distributed Hessian Free Algorithm for Large-scale Empirical Risk Minimization via Accumulating Sample Strategy (2018, methodology): “Due to the structure of matrix P , and as it is discussed in [Ma and Tak´aˇc, 2016], this matrix can be considered as |A n | rank 1 updates on a diagonal matrix, and Set w n = ˜ w k 12: end while now, using Woodbury Formula [Press et al., 2007] is a very eﬃcient way to solve the mentioned system.”
SDSS-IV MaNGA : spatially resolved star formation histories in galaxies as a function of galaxy mass and type (2016, methodology): “Errors on the gradients are calculated using a Monte Carlo bootstrap resampling method (Press et al. 2007).”
Data-driven modelling: some past experiences and new approaches (2008, methodology): “gradient or Broydon–Fletcher–Goldfarb–Shanno (BFGS) methods (Press et al. 2007).”
Semiparametric Mean Field Variational Bayes: General Principles and Numerical Issues (2016, unknown): “Details of the nonlinear conjugate gradient method are given in Section 10.8 of Press et al. (2007).”
A real-time system for biomechanical analysis of human movement and muscle function (2013, methodology): “The nonlinear optimization problem in (1) was solved with the Levenberg–Marquardt algorithm [20], with a Jacobian matrix for the forward kinematic model that was generated by symbolical differentiation in Autolev.”
In situ spectroscopic ellipsometry as a versatile tool for studying atomic layer deposition (2009, background): “Ideally, a good fit should result in a χ2 close to 1 [34, 35].”