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Related Concept Videos

Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the key values are 3...
Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
Definition of z-Transform01:26

Definition of z-Transform

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
Complex Zeros01:29

Complex Zeros

Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...

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Related Experiment Video

Updated: Jun 5, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Modified Z-algorithms for reckoning fixed points with application to nonlinear integral equations.

Habib Ur Rehman1, Hasanen A Hammad2,3, Manal Elzain Mohamed Abdalla4

  • 1School of Mathematics, Yunnan Normal University, Kunming, China.

Plos One
|June 3, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces the Z-iteration method to find common fixed points for nonexpansive mappings. The new algorithm proves effective for both theoretical convergence and solving nonlinear integral equations in Banach spaces.

Related Experiment Videos

Last Updated: Jun 5, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Functional Analysis
  • Nonlinear Analysis
  • Numerical Analysis

Background:

  • Fixed-point theory is crucial for solving equations.
  • Nonexpansive mappings are a key class of functions in analysis.
  • Finding common fixed points for multiple mappings is challenging.

Purpose of the Study:

  • To investigate the existence of common fixed points for pairs of nonexpansive mappings.
  • To develop a novel iterative scheme for this purpose.
  • To demonstrate the practical application of the scheme.

Main Methods:

  • Introduction of a new four-step iterative scheme: the Z-iteration.
  • Establishment of weak and strong convergence theorems.
  • Application to approximate solutions of nonlinear integral equations.

Main Results:

  • The Z-iteration scheme guarantees the existence of common fixed points.
  • Demonstrated weak and strong convergence properties of the scheme.
  • Successful approximation of solutions for nonlinear integral equations in Banach spaces.

Conclusions:

  • The Z-iteration is a powerful tool for finding common fixed points.
  • The method offers a practical approach to solving complex equations.
  • Theoretical convergence results are validated by constructive and applied examples.