I was just wondering what defined the domain of a Lagrange interpolating polynomial. Is it the domain of the function being interpolated? Always the reals? I am asking this as I have constructed a function using polynomial interpolation and I want to know if I can just give it a complex valued input. Is that rigourous?
2026-03-25 06:00:43.1774418443
Domain of an interpolated polynomial function
30 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ANALYSIS
- Analytical solution of a nonlinear ordinary differential equation
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Show that $d:\mathbb{C}\times\mathbb{C}\rightarrow[0,\infty[$ is a metric on $\mathbb{C}$.
- conformal mapping and rational function
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Elementary question on continuity and locally square integrability of a function
- Proving smoothness for a sequence of functions.
- How to prove that $E_P(\frac{dQ}{dP}|\mathcal{G})$ is not equal to $0$
- Integral of ratio of polynomial
Related Questions in FUNCTIONS
- Functions - confusion regarding properties, as per example in wiki
- Composition of functions - properties
- Finding Range from Domain
- Why is surjectivity defined using $\exists$ rather than $\exists !$
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Lower bound of bounded functions.
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
Related Questions in INTERPOLATION
- Almost locality of cubic spline interpolation
- Reverse Riesz-Thorin inequality
- How to construct a B-spline from nodal point in Matlab?
- Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
- Show that there is a unique polynomial of degree at most $2k+1$ such that $p^{[j]}(x_1)=a_j \text{ and } p^{[j]}(x_2)=b_j \text{ for } j=0,\dots, k.$
- How to find x intercept for a polynomial regression curve(order 7)
- Quadrature rules estimation
- How to obtain generalized barycentric coordinates for n-sided polygon?
- the highest degree of the polynomial, for which the above formula is exact?
- Interpolation method that gives the least arc lenght of the curve.
Related Questions in LAGRANGE-INTERPOLATION
- Questions about a proof of the existence of the Lagrange polynomial
- Polynomial interpolation with data points from derivative of original polynomial
- Find the error of using an interpolating polynomial of degree 20 to approximate e^−x
- Lagrange linear, quadratic, and cubic interpolations maximum interpolation error functions comparison
- Interpolation using multiple neighboring points
- Lagrange interpolation of multivariate polynomials
- Can I decompose the Lagrange interpolating polynomial of the sum of 2 functions into 2 separate Lagrange polynomials?
- What is the Lagrange Interpolation polynomial of $1/{(x-1)}$?
- Find polynomial $q(x)$ whose values match a known polynomial $p(x)$ with matching values except one.
- Accuracy of Lagrange polynomial
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?