Best approximation, Tikhonov regularization and reproducing kernels

DOI10.2996/kmj/1123767016zbMath1087.65053OpenAlexW2003815044MaRDI QIDQ2574400

Saburou Saitoh

Publication date: 21 November 2005

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1123767016

zbMATH Keywords

stabilityinverse problemserror boundsbest approximationlinear ill-posed problemslinear operator equationsMoore-Penrose inversereproducing kernel Hilbert spaceleast-squares solutionsTikhonov regulariztaion

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (24)

Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem ⋮ Solving Fredholm integral equation of the first kind using Gaussian process regression ⋮ Reproducing inversion formulas for the Dunkl-Wigner transforms ⋮ Whittaker-Stockwell transform and Tikhonov regularization problem ⋮ Fock-type spaces associated to higher-order Bessel operator ⋮ Reproducing kernel theory associated with the generalized Stockwell transform and applications ⋮ Localization operators and inversion formulas for the Dunkl-Weinstein-Stockwell transform ⋮ Reproducing kernel Hilbert spaces (RKHS) for the higher order Bessel operator ⋮ Difference and primitive operators on the Dunkl-type Fock SPACE \(\mathscr{F}_{\alpha }(\mathbb{C}^d)\) ⋮ Uncertainty principles and extremal functions for the Dunkl \(L^2\)-multiplier operators ⋮ Calderón's reproducing formulas and extremal functions for the Riemann-Liouville \(L^2\)-multiplier operators ⋮ Dirichlet principle using computers ⋮ Some examples of extremal functions on the Dunkl-type Fock space \(F_k(\mathbb C)\) ⋮ Operators and Tikhonov regularization on the Fock space ⋮ Analytical and numerical approximation formulas on the Dunkl-type Fock spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Analytical and numerical approximation formulas for the Fourier multiplier operators ⋮ DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION ⋮ Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces ⋮ Inversion formulas for the Dunkl-type Segal–Bargmann transform ⋮ Unnamed Item ⋮ APPLICATIONS ON THE BESSEL-STRUVE-TYPE FOCK SPACE ⋮ Analytical and numerical applications for the Fourier multiplier operators on ℝⁿ× (0, ∞)

This page was built for publication: Best approximation, Tikhonov regularization and reproducing kernels