Numerical differentiation is a technique used to approximate the derivative of a function based on discrete data points, rather than relying on analytical methods. This approach is particularly useful when dealing with functions that are difficult to differentiate analytically or when only a set of sampled points is available, such as experimental or observational data.

A Radial Basis Function (RBF) is a real-valued function whose value depends only on the distance from a center point, typically in a multi-dimensional space. RBFs are used in various applications, including interpolation, function approximation, and machine learning, particularly in radial basis function networks and support vector machines. ### Key Characteristics: 1. **Distance-Based**: The function typically measures the distance from a point in space to a center point (also called a basis center).

Relative change and absolute change (often referred to simply as "difference") are two ways to express changes in a value, and they serve different purposes in analysis. ### Absolute Change (Difference) - **Definition**: Absolute change refers to the straightforward difference between two values.

A Riemann solver is a numerical method used to solve hyperbolic partial differential equations (PDEs) that arise in various applications, such as fluid dynamics, gas dynamics, and traffic flow. The term "Riemann problem" refers to an initial value problem for a conservation law which consists of a hyperbolic PDE with piecewise constant initial data — typically defined by two constant states separated by a discontinuity.

Shanks' transformation (also known as Shanks's transformation or the Shanks transform) is a technique used in numerical analysis to accelerate the convergence of sequences. It is particularly useful in cases where a sequence converges slowly to a limit. The transformation is named after the mathematician Daniel Shanks, who introduced it in the context of numerical approximations.

Stechkin's lemma is a result in the field of functional analysis and approximation theory, particularly concerning the properties of certain sequences of functions and their convergence. It is often referenced in the context of studying the approximation of functions in terms of series expansions and the behavior of polynomials. The lemma generally states conditions under which a sequence of functions (often approximating polynomials or Fourier series) converges uniformly to a continuous function.

An online algorithm is a type of algorithm that processes its input piece by piece, in a serial fashion, without having complete knowledge of the entire input in advance. This means that the algorithm makes decisions based on the information it has received up to that point, rather than waiting to receive all the data before making a decision. Online algorithms are commonly used in scenarios where data arrives in real-time or where it's impractical to store and manage all the input data at once.

Optimal scheduling refers to the process of arranging tasks, events, or resources in a way that maximizes efficiency or effectiveness while minimizing costs or delays. This concept can be applied across various fields, including manufacturing, project management, resource allocation, transportation, and computing. The goal of optimal scheduling is typically to achieve an ideal balance among competing objectives, such as: 1. **Time Efficiency**: Minimizing the time required to complete tasks or projects.

The Berndt–Hall–Hall–Hausman (BHHH) algorithm is an optimization technique used for maximum likelihood estimation (MLE) in statistical models, particularly in the context of econometrics. It is named after economists Richard Berndt, Bruce Hall, Robert Hausman, and Jerry Hausman, who contributed to its development and application.

The Segner wheel, also known as the Segner wheel or water wheel, is a type of hydraulic machine invented by the German engineer Jacob Segner in the 18th century. It is primarily a water-driven turbine, designed to convert the kinetic energy of flowing water into mechanical energy. The Segner wheel consists of a horizontal wheel with a series of curved blades or cups attached to its circumference. Water flows over these blades, causing the wheel to rotate.

"Segundo Romance" is a famous song by the renowned Argentinian tango composer and singer, Facundo Cabral. Released in 1974, it's known for its poetic lyrics and emotive melodies typical of tango music. The song is a follow-up to Cabral's earlier work, serving as a reflection on love, loss, and the complexities of relationships.

The Chambolle-Pock algorithm is a powerful method for solving optimization problems that involve a combination of convex functions and Bregman distances. It is particularly useful for problems that can be framed as finding a minimizer of a convex function subject to certain constraints.

Column Generation is an optimization technique used primarily in solving large-scale linear programming (LP) and integer programming problems. It is especially useful for problems with a large number of variables, where explicitly representing all variables is computationally infeasible.

Destination dispatch is an advanced elevator control system designed to improve the efficiency and speed of vertical transportation in buildings, particularly in high-rise structures. Unlike traditional elevator control systems that manage cars based on call buttons for up or down, destination dispatch systems take a more integrated approach to optimize elevator trips. ### How It Works 1. **User Input**: When a passenger enters the lobby or any other call area, they enter their desired floor on a touchscreen or similar interface.

The Great Deluge algorithm is a metaheuristic optimization technique inspired by the concept of a flood or deluge used to manage and explore search spaces. It is particularly useful for solving combinatorial optimization problems, where the goal is to find the best solution from a finite set of possible solutions. ### Key Concepts: 1. **Search Space**: The algorithm navigates through a potential solution space, similar to how water would rise and cover terrain, altering the landscape of possible solutions.

Lexicographic max-min optimization is a method used in multi-objective optimization problems where multiple criteria are involved. The approach prioritizes the objectives in a lexicographic order, meaning that the most important objective is optimized first. If there are multiple solutions for the first objective, the second most important objective is then optimized among those solutions, and this process continues down the list of objectives.

The MM algorithm, or the "Minorization-Maximization" algorithm, is an optimization technique often used in mathematical optimization, statistics, and machine learning. The key idea behind the MM algorithm is to solve complex optimization problems by breaking them down into a series of simpler subproblems.

Ternary search is a divide-and-conquer search algorithm that is used to find the maximum or minimum value of a unimodal function. A unimodal function is defined as one that has a single local maximum or minimum within a given interval. Ternary search divides the search interval into three parts, which results in two midpoints, and then eliminates one of the three segments based on the comparison of the function values at these midpoints.

Tree rearrangement generally refers to the processes or operations involved in modifying the structure or topology of a tree data structure. This term can be applied in different contexts, such as in computer science, graph theory, and even in evolutionary biology. Here are some contexts where tree rearrangement is relevant: 1. **Tree Data Structures**: In computer science, tree rearrangement might involve operations like rotations, balancing (as in AVL or Red-Black trees), or merging trees.

Zadeh's rule refers to a concept in fuzzy logic developed by Lotfi Zadeh, who is known as the father of fuzzy set theory. While Zadeh himself did not specifically codify a "Zadeh's rule," the term is often associated with a fundamental principle in fuzzy logic related to the combination of fuzzy sets and the reasoning process within this framework.