I have been using Aitken's construction in my work. I have seen several references to the construction but never a direct reference to an article in a Journal. I am preparing a comprehensive report to show the direct equivalence of the construction to the second-order Lagrange polynomial. I will be including an extension of the construction that generates the local slopes at points on the parabola.
2026-04-03 12:34:53.1775219693
Do you know of a reference for Aitken's graphical construction of points on a Parabola?
42 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in POLYNOMIALS
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Integral Domain and Degree of Polynomials in $R[X]$
- Can $P^3 - Q^2$ have degree 1?
- System of equations with different exponents
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Dividing a polynomial
- polynomial remainder theorem proof, is it legit?
- Polyomial function over ring GF(3)
- If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?
- $x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Minimum of the 2-norm
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
Related Questions in GRAPHING-FUNCTIONS
- Lower bound of bounded functions.
- Do Irrational Conjugates always come in pairs?
- Graph rotation: explanation of equation
- Plot function y = tan(yx)
- Sketching a lemniscate curve with a max function?
- 3 points on a graph
- show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$
- What is this method of sketching a third degree curve?
- Getting a sense of $f(x) = x (\log x)^6$
- Can I describe an arbitrary graph?
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.
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?
I was able to find my answer. https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/on-interpolation-by-iteration-of-proportional-parts-without-the-use-of-differences/482BBF2A12045CB996628BE8C5B42FFC
Aitken, A. (1932). On Interpolation by Iteration of Proportional Parts, without the Use of Differences. Proceedings of the Edinburgh Mathematical Society, 3(1), 56-76. doi:10.1017/S0013091500013808
Regards Alfred Here are more details about Aitken's Construction. https://www.dropbox.com/s/hhtos2l85wa0qfr/Aitken%E2%80%99s%20Graphical%20Construction%20for%20a%20Parabola%20V4.pdf?dl=0 https://www.dropbox.com/s/iv6d52uymu3xslv/Step%20by%20Step%20%20Aitken%20Construction.pdf?dl=0