# Tagged Questions

Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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### Representability of smooth invertible Lipschitz functions by a finite composition of near-identity functions

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### On different norms of the interpolating operator

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### Find $p$ s.t. there is a sequence of nodes in $[0,1]$ s.t. sequence of interpolating polynomials of every continuous function converges in $p$-norm

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### Minimax Approximation to Sine Function on interval [-K, K]

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### Does log-concave approximable distribution satisfy transportation-cost inequality?

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### Given any sequence of interpolating nodes, can we find a continuous function $f$ whose interpolating polynomials doesn't converge to $f$ point-wise

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### Approximate a function by smooth functions with bounded below second-order derivative

**3**

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### Given a local metric which is $C^1$-close to another, can we extend it globally while preserving the approximation?

**3**

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### Is the kernel of a Fredholm operator stable under perturbation?

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### Approximate in $W_1$ sense, an empirical distribution with restriction of true distribution on a set

**4**

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### Can we stay invertible while approximating linear maps in Sobolev spaces?

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### Giving Uniform Bound on Differences of Sums of Converging Polynomials

**8**

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### Degree of 2-variable real polynomial that’s large on a square and small on a nearby “L”

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### Can a continuous map on a Hilbert manifold be approximated by a map which has infinitely many critical points?

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### On effective constructions in the functional analysis of Volterra's integration operator

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### Approximating norms using numerical integration? [closed]

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### What are the compact elements in the domain of functions on the Interval Domain, [D,D]?

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### Continuity of solution to 2nd Order PDE w.r.t. the coefficients

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### dense subalgebra in measurable functions set

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### Intersection of Sobolev space with the space of continuous functions

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### automorphisms of a measurable space can be approximated by continuous measure preserving maps?

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### Bounded polynomial having coefficients that are bounded linearly in degree and number of variables

**9**

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### Real polynomial bounded at inverse-integer points

**5**

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### Padé multipoint approximants of the exponential function

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**1**answer

### Approximation of a continuous function by a smooth one on an open set

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### Bounding quantiles of the noncentral chi distribution

**5**

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### What are the possible $L^{\infty}$ closures of an integration-invariant linear subspace of $C([0,1],\mathbb{R})$?

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### Role of polyhedral domain in convergence of finite element method

**4**

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### approximating the $|x|$ function

**3**

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### Normal approximation to the pointwise/Hadamard/Schur product of two multivariate Gaussian/normal random variables

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### Optimal $L^2$ bounds of cubic spline interpolation

**3**

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### Closure of polynomials of a function in $L^2$

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### Holes of a compact set in $\mathbb{R}^n$ that do not contain holes of a larger open set

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### Finding a tight upper bound of $\int_0^\infty e^{-a\sqrt{1-e^{-x}}-x^2/2} dx$ as a function of $a$, $a>0$

**2**

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### Approximation error of 1-Lipschitz function on cubical mesh

**3**

**2**answers

### Finding a tight upper bound of $\int_0^\infty e^{-x^2/2-a(1-e^{-x})}dx,\ a>0$, as a function of $a$

**2**

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### A good starting position for maximizing a function with Newton-Raphson / Halley's method

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### What are good ways to 'relax' a uniform approximation into independent saddle-point expressions once the uniform approach is no longer needed?

**2**

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### Approximately complemented subspaces

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### Approximating a compact $C^1$ hypersurface without boundary

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### Literature Request: Finite Dimensional “Approximations” of Linear Operators

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### Integral of exponential of quadratics + exponentials

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### Can Carlsons's iterative algorithm for $\arctan x$ be inverted to get one for $\tan x$?

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### Truncation error of product and composition of functions?

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### Approximating partial $p$-series

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### Tight L2 bound on moments approximation and reference

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### Is it possible to estimate number of the tuples?

**1**

**2**answers

### Cubic interpolating Spline - Number of extremum points

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### Pade approximation of a rational function

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