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Parameter Choices for Fast Harmonic Spline Approximation (Q3120070)

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Language	Label	Description	Also known as
English	Parameter Choices for Fast Harmonic Spline Approximation	scientific article

Statements

scholarly article

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Parameter Choices for Fast Harmonic Spline Approximation (English)

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Handbook of Mathematical Geodesy

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publication date

1 March 2019

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zbMATH Keywords

spline approximation

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fast multipole methods

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-319-57181-2_9

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Theory of Reproducing Kernels

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Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion

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Some considerations concerning regularization and parameter choice algorithms

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A Lepskij-type stopping rule for regularized Newton methods

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The quasi-optimality criterion for classical inverse problems

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Recent results on the quasi-optimality principle

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Comparing parameter choice methods for regularization of ill-posed problems

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Optimal regularization for ill-posed problems in metric spaces

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Regularization without preliminary knowledge of smoothness and error behaviour

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Regularization independent of the noise level: an analysis of quasi-optimality

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Iteratively Regularized Gauss–Newton Method for Nonlinear Inverse Problems with Random Noise

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Regularization of statistical inverse problems and the Bakushinskiĭ veto

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Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration

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\(L\)-curve curvature bounds via Lanczos bidiagonalization

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Modern statistical estimation via oracle inequalities

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A Fast Adaptive Multipole Algorithm for Particle Simulations

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Nonparametric statistical inverse problems

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Oracle inequalities for inverse problems

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Block Thresholding and Sharp Adaptive Estimation in Severely Ill-Posed Inverse Problems

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A fast adaptive multipole algorithm in three dimensions

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Approximation of method of regularization estimators

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Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation

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Confidence Intervals for Nonparametric Curve Estimates

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Improved estimates of statistical regularization parameters in Fourier differentiation and smoothing

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Selection criteria for scatterplot smoothers

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A posteriori parameter choice for general regularization methods for solving linear ill-posed problems

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Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations

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Sparse regularization of inverse gravimetry—case study: spatial and temporal mass variations in South America

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On spherical spline interpolation and approximation

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Spline methods in geodetic approximation problems

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Spherical spline interpolation - basic theory and computational aspects

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A spline interpolation method for solving boundary value problems of potential theory from discretely given data

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Special functions of mathematical (geo-)physics

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Multiscale potential theory. With applications to geoscience

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Special Functions in Mathematical Geosciences: An Attempt at a Categorization

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A survey on spherical spline approximation

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Spherical panel clustering and its numerical aspects

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An A Posteriori Parameter Choice for Ordinary and Iterated Tikhonov Regularization of Ill-Posed Problems Leading to Optimal Convergence Rates

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A fast ``Monte-Carlo cross-validation'' procedure for large least squares problems with noisy data

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Asymptotic comparison of (partial) cross-validation, GCV and randomized GCV in nonparametric regression

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Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observa\-tions

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Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter

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A fast algorithm for particle simulations

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Smoothing spline ANOVA models

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Fast multipole accelerated solution of the oblique derivative boundary value problem

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On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data

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Analysis of Discrete Ill-Posed Problems by Means of the L-Curve

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The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems

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An adaptive pruning algorithm for the discrete L-curve criterion

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Analysis of Profile Functions for General Linear Regularization Methods

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Regularization of exponentially ill-posed problems

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A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines

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Smoothing noisy data with spline functions

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Fast summation of radial functions on the sphere

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Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems

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On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization

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Smoothers and the<i>C<sub>p</sub></i>, Generalized Maximum Likelihood, and Extended Exponential Criteria

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Justification of the choice of regularization parameter according to quasi-optimality and quotient criteria

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On a Problem of Adaptive Estimation in Gaussian White Noise

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Asymptotic optimality of \(C_ L\) and generalized cross-validation in ridge regression with application to spline smoothing

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Asymptotic optimality for \(C_ p\), \(C_ L\), cross-validation and generalized cross-validation: Discrete index set

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Heuristic parameter selection based on functional minimization: Optimality and model function approach

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Discrepancy based model selection in statistical inverse problems

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Convergence Rates for Regularized Solutions

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Asymptotic optimality of generalized cross-validation for choosing the regularization parameter

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On the discrepancy principle and generalised maximum likelihood for regularisation

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Comparisons of parameter choice methods for regularization with discrete noisy data

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Robust generalized cross-validation for choosing the regularization parameter

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Strong robust generalized cross-validation for choosing the regularization parameter

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Robust GCV choice of the regularization parameter for correlated data

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Statistical Inverse Estimation in Hilbert Scales

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What do we learn from the discrepancy principle?

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Geometry of linear ill-posed problems in variable Hilbert scales

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Regularization of some linear ill-posed problems with discretized random noisy data

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Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball

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Classical Physical Geodesy

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Morozov's discrepancy principle under general source conditions

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The convergence of a new heuristic parameter selection criterion for general regularization methods

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Morozov's discrepancy principle for tikhonov

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A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

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Fast Summation at Nonequispaced Knots by NFFT

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On the quasioptimal regularization parameter choices for solving ill-posed problems

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A Regularization Parameter in Discrete Ill-Posed Problems

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Making robust the cross-validatory choice of smoothing parameter in spline smoothing regression

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Rapid solution of integral equations of classical potential theory

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A cautionary note about crossvalidatory choice

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Use of the regularization method in non-linear problems

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On the best rate of adaptive estimation in some inverse problems

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Computational Methods for Inverse Problems

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Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

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Spline Interpolation and Smoothing on the Sphere

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When is the optimal regularization parameter insensitive to the choice of the loss function?

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Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-57181-2_9

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3120070

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