Fushuai Jiang

activity

20192026

C^{2} (R^{2})

Interpolation

8 citations · 9 across the 12 of their papers we have counts for

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8 papers · 1 filter

math.CA2026

Semialgebraic $C^{m}$ solutions to a univariate system of linear inequalities with Nash forcing

Fushuai Jiang, Garving K. Luli

Let $(A_{ij} (x))_{1 \leq i \leq N, 1 \leq j \leq M}$ be a matrix of univariate semialgebraic functions. We study the solvability of the system of linear inequalities \begin{equatio…

math.CA2026

Smooth solutions to systems of linear inequalities on $R$

Fushuai Jiang, Garving K. Luli

Fix an integer $m \geq 0$ . We study the one-dimensional problem of deciding when a system of linear inequalities \begin{equation*} \sum_{j=1}^M A_{ij}(x)F_j(x)\leq f_i(x),\qquad i=1…

math.CA2026

Optimal $C^{1, 1}$ and Quasi-Optimal $C^{2}$ Monotone Interpolation with Curvature Control

Fushuai Jiang, Garving K. Luli

We study monotone Hermite interpolation on an interval, where both function values and first derivatives are prescribed at the nodes. Among all $C^{1, 1}$ interpolants, we seek one…

math.CA2021

$C^{2}$ Interpolation with Range Restriction

Charles Fefferman, Fushuai Jiang, Garving K. Luli

Given $- \infty < λ < Λ < \infty$ , $E \subset R^{n}$ finite, and $f : E \to [λ, Λ]$ , how can we extend $f$ to a $C^{m} (R^{n})$ function $F$ such that $ λ\leq F \…

math.CA2021★ 8 cited

Algorithms for Nonnegative $C^{2} (R^{2})$ Interpolation

Fushuai Jiang, Garving K. Luli

Let $E \subset R^{2}$ be a finite set, and let $f : E \to [0, \infty)$ . In this paper, we address the algorithmic aspects of nonnegative $C^{2}$ interpolation in the plane.…

math.CA2020

$C^{2} (R^{2})$ Nonnegative Extension by Bounded-depth Operators

Fushuai Jiang, Garving K. Luli

In this paper, we prove the existence of a nonnegative parameter-dependent (nonlinear) $C^{2} (R^{2})$ extension operator with bounded depth.

math.CA2019

Nonnegative Whitney Extension Problem for $C^{1} (R^{n})$

Fushuai Jiang

Let $f$ be a real-valued function on a compact subset in $R^{n}$ . We show how to decide if $f$ extends to a nonnegative and $C^{1}$ function on $R^{n}$ . There…

math.CA2019

Nonnegative $C^{2} (R^{2})$ interpolation

Fushuai Jiang, Garving K. Luli

In this paper, we prove two improved versions of the Finiteness Principle for nonnegative $C^{2} (R^{2})$ interpolation, previously proven by Fefferman, Israel, and Luli. The…

Semialgebraic Cm solutions to a univariate system of linear inequalities with Nash forcing

Smooth solutions to systems of linear inequalities on R

Optimal C1,1 and Quasi-Optimal C2 Monotone Interpolation with Curvature Control

C2 Interpolation with Range Restriction

Algorithms for Nonnegative C2(R2) Interpolation

C2(R2) Nonnegative Extension by Bounded-depth Operators

Nonnegative Whitney Extension Problem for C1(Rn)

Nonnegative C2(R2) interpolation

Semialgebraic $C^{m}$ solutions to a univariate system of linear inequalities with Nash forcing

Smooth solutions to systems of linear inequalities on $R$

Optimal $C^{1, 1}$ and Quasi-Optimal $C^{2}$ Monotone Interpolation with Curvature Control

$C^{2}$ Interpolation with Range Restriction

Algorithms for Nonnegative $C^{2} (R^{2})$ Interpolation

$C^{2} (R^{2})$ Nonnegative Extension by Bounded-depth Operators

Nonnegative Whitney Extension Problem for $C^{1} (R^{n})$

Nonnegative $C^{2} (R^{2})$ interpolation