Solutions of ill-posed problems

By A. Tikhonov, Vasiliy Yakovlevich Arsenin. 1977

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “, 2013; Cho, 2014), and through Tikhonovtype (Tikhonov et al., 1977) regularization of RBMs (Cho et al.”
Kernels for Vector-Valued Functions: a Review (2011, background): “Then the posterior distribution is proportional to e −( 1 σ2 ‖fw(X)−Y‖ 2 n+‖w‖ (2)) , and we see that a maximum a posteriori estimate will in turn give the minimization problem defining Tikhonov regularization [98], where the regularization parameter is now related to the noise variance.”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “Gaussian processes are among a class of methods known as kernel machines (see [8, 9, 10]) and are analogous to regularization approaches (see [11, 12, 13]).”
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations (2017, background): “Moreover, Gaussian processes are among a class of methods known as kernel machines (see [31, 36, 37]) and are analogous to regularization approaches (see [21, 34, 35]).”
Machine learning of linear differential equations using Gaussian processes (2017, background): “Moreover, Gaussian processes are among a class of methods known as kernel machines (see [51,44,49]) and have analogies with regularization approaches (see [47,48,36]).”
Learning from labeled and unlabeled data on a directed graph (2005, methodology): “This work is the discrete analogue of classic regularization theory (Tikhonov & Arsenin, 1977; Wahba, 1990).”
Networks and the best approximation property (1990, methodology): “Existence and uniqueness of best approximation for regularization and RBF One of the possible approaches to the problem of surface reconstruction is given by regularization theory (Tikhonov and Arsenin, 19777 Bertero et al. 1988).”
From wrinkles to creases in elastomers: the instability and imperfection-sensitivity of wrinkling (2012, methodology): “A the damping factor c here is similar to that of the regularization factor in the Tikhonov regularization method (Tikhonov & Arsenin 1977), which is widely used to deal with ill-posed inverse problems.”
Bias-corrected regularized solution to inverse ill-posed models (2012, background): “For some more details on inverse problem theory, the reader may refer to, e.g., Tikhonov and Arsenin (1977), Tikhonov et al. (1995), Morozov (1984) and Tarantola (2005).”
Pattern Recognition and Machine Learning (2006, unknown): “which is known as Tikhonov regularization (Tikhonov and Arsenin, 1977; Bishop, 1995b).”
A Blur-Robust Descriptor with Applications to Face Recognition (2012, methodology): “Regularization methods based on total variation [27] and Tikhonov regularization [31] constitute an integral part of this process.”
Some Properties of Regularized Kernel Methods (2004, methodology): “As shown by Evgeniou et al. (2000) the above minimization problem can also be seen as particular instance of Tikhonov Regularization (Tikhonov and Arsenin, 1977; Mukherjee et al., 2002) for a multivariate function approximation problem which is well known to be ill-posed (Bertero et al., 1988; Evgen”
Variance Component Estimation in Linear Inverse Ill-posed Models (2006, background): “Hoerl and Kennard 1970; Tikhonov and Arsenin 1977; Xu 1992; Koch and Kusche 2002) or truncated singular value decomposition (see e.g.”
Support Vector Machines with Applications (2006, methodology): “The widest used setting minimizes Tikhonov’s regularization functional [73], which consists of solving the optimization problem”
Multicategory Proximal Support Vector Machine Classifiers (2005, methodology): “We note that the PSVM formulation (2) can be also interpreted as a regularized least squares solution [34] of the system of linear equations D(Aw − eγ) = e, that”
A new improved regularization method for dynamic load identification (2014, methodology): “There have been some traditional and classic regularization methods, such as the famous Tikhonov method,[13] the truncated singular value decomposition (TSVD),[14] the modified TSVD,[15] the damped SVD,[16] the iterative regularisation methods [17] and so forth.”