For a lot of smooth functions, you could use the Argument Principle. However, those only work for holomorphic functions. Functions with the floor function are not holomorphic. So, given a smooth function that uses the floor function, is there a method similar to the Argument Principle, that can numerically tell the number of roots of the function in an interval?
2026-03-27 10:09:15.1774606155
Numerically Finding Number of Roots in an Interval of a Smooth Function involving Floor Function
55 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in ROOTS
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Roots of a complex equation
- Do Irrational Conjugates always come in pairs?
- For $f \in \mathbb{Z}[x]$ , $\deg(\gcd_{\mathbb{Z}_q}(f, x^p - 1)) \geq \deg(\gcd_{\mathbb{Q}}(f, x^p - 1))$
- The Heegner Polynomials
- Roots of a polynomial : finding the sum of the squares of the product of two roots
- Looking for references about a graphical representation of the set of roots of polynomials depending on a parameter
- Approximating the first +ve root of $\tan(\lambda)= \frac{a\lambda+b}{\lambda^2-ab}$, $\lambda\in(0,\pi/2)$
- Find suitable scaling exponent for characteristic polynomial and its largest root
- Form an equation whose roots are $(a-b)^2,(b-c)^2,(c-a)^2.$
Related Questions in CEILING-AND-FLOOR-FUNCTIONS
- System of simultaneous equations involving integral part (floor)
- Is there a limit?
- Largest value of sequence
- Does $x+\sqrt{x}$ ever round to a perfect square, given $x\in \mathbb{N}$?
- Fractional part of integer multiples
- Proof regarding the ceiling function.
- Find number of solutions of $(x-1)^2+\lceil x \rceil=4$
- Let $n$ is a natural number. Find $\int_0^n 2x \lfloor x \rfloor dx$
- Inverse cosine inside floor function derivative
- Floor function problem
Related Questions in SMOOTH-FUNCTIONS
- Connecting smooth functions in a smooth way
- Is the restriction (to lower dimensions) of a smooth function still smooth?
- Understanding the proof of the Concentration-Compactness principle
- Does an integral inequality imply a pointwise inequality?
- A weird definition of regular function
- Are charts for smooth manifolds homeomorphisms or diffeomorphisms?
- Find a sequence $(\phi_n)_n \subset C^{\infty}_c(\mathbb{R}^N)$ which converges in both $L^p(\nu)$ and $L^q(\mu)$ to $1_E$
- Straight Lines are Strict Minimizers of Arclength in Euclidean Space
- Several Questions on Smooth Urysohn's Lemma
- For what functions is $\lim_{n\to \infty}|f^{(n)}(x)|=0$? (Where $f^{(n)}(x)$ is the $n$th derivative of $f$)
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?