Smooth Interpolation of Data by Efficient Algorithms

Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative

“…See for example Proposition 2 of [4]. Using the particular construction in this proof, we can take C = 6.…”

Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative

“…See for example Proposition 2 of [4]. Using the particular construction in this proof, we can take C = 6.…”

On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment

“…The papers [62,63,64,65] and the references cited therein detail a complete solution to Problem (W). Observe that X ⊂ R D is arbitrary.…”

“…The papers [62,63,64,65] and the references cited therein have been extended to handle other map spaces as well as to increase understanding of various problems on the borders of data science, approximation theory and algebraic geometry. For example, aspects of constrained approximation, finiteness principles, finte selections, interpolation, sobolev approximation and smooth selection.…”

Efficient Second-Order Shape-Constrained Function Fitting

“…[24] describes (multidimensional) L 2 convex regression algorithms based quadratic programming. Fefferman [8] studied a closely related problem of smooth interpolation of data in Euclidean space minimizing a certain norm defined on the derivatives of the function. His setup is much more general, but his algorithm cannot find arbitrarily good interpolations (ε is fixed for the algorithm).…”

Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative

“…See for example Proposition 2 of [4]. Using the particular construction in this proof, we can take C = 6.…”

On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment

“…The papers [62,63,64,65] and the references cited therein detail a complete solution to Problem (W). Observe that X ⊂ R D is arbitrary.…”

“…The papers [62,63,64,65] and the references cited therein have been extended to handle other map spaces as well as to increase understanding of various problems on the borders of data science, approximation theory and algebraic geometry. For example, aspects of constrained approximation, finiteness principles, finte selections, interpolation, sobolev approximation and smooth selection.…”

Efficient Second-Order Shape-Constrained Function Fitting

“…[24] describes (multidimensional) L 2 convex regression algorithms based quadratic programming. Fefferman [8] studied a closely related problem of smooth interpolation of data in Euclidean space minimizing a certain norm defined on the derivatives of the function. His setup is much more general, but his algorithm cannot find arbitrarily good interpolations (ε is fixed for the algorithm).…”

Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative

“…See for example Proposition 2 of [4]. Using the particular construction in this proof, we can take C = 6.…”

On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment

“…The papers [62,63,64,65] and the references cited therein detail a complete solution to Problem (W). Observe that X ⊂ R D is arbitrary.…”

“…The papers [62,63,64,65] and the references cited therein have been extended to handle other map spaces as well as to increase understanding of various problems on the borders of data science, approximation theory and algebraic geometry. For example, aspects of constrained approximation, finiteness principles, finte selections, interpolation, sobolev approximation and smooth selection.…”

Efficient Second-Order Shape-Constrained Function Fitting

“…[24] describes (multidimensional) L 2 convex regression algorithms based quadratic programming. Fefferman [8] studied a closely related problem of smooth interpolation of data in Euclidean space minimizing a certain norm defined on the derivatives of the function. His setup is much more general, but his algorithm cannot find arbitrarily good interpolations (ε is fixed for the algorithm).…”