A "stranded asset" refers to a resource or investment that has experienced a sudden or gradual loss of its economic value, often due to changing market dynamics, regulatory environments, or technological advancements. These assets can no longer earn an economic return, and as a result, they may become liabilities for their owners.

Unintended consequences refer to outcomes that are not the ones originally intended or anticipated when an action is taken. These consequences can be positive, negative, or neutral and often arise from the complexity of systems in which various factors interact in unforeseen ways. Unintended consequences can occur in many contexts, including policy-making, economics, social behavior, and environmental issues. For example: 1. **Policy-making**: A government might implement a subsidy for a specific industry to boost job creation.

Level set methods are a numerical technique for tracking interfaces and shapes in computational mathematics and computer vision. They are particularly used in multiple fields, including fluid dynamics, image processing, and computer graphics. The fundamental idea behind level set methods is to represent a shape or an interface implicitly as the zero level set of a higher-dimensional function, often called the level set function.

Numerical analysis is a branch of mathematics that focuses on techniques for approximating solutions to mathematical problems that may not have closed-form solutions. Here’s a list of key topics commonly covered in numerical analysis: 1. **Numerical Methods for Solving Equations:** - Bisection Method - Newton's Method - Secant Method - Fixed-Point Iteration - Root-Finding Algorithms 2.

Uncertainty propagation software is used to quantify the uncertainty in output values based on uncertainties in input variables. This is particularly important in fields such as engineering, risk analysis, and scientific research, where understanding the uncertainty can significantly affect decision-making. Below is a list of popular software tools that are used for uncertainty propagation: 1. **MATLAB** - Offers various toolboxes like the Statistics and Machine Learning Toolbox for uncertainty analysis.

Model Order Reduction (MOR) refers to a set of techniques and methods used to simplify complex mathematical models while preserving essential features, behaviors, or properties. These techniques are particularly valuable in fields such as engineering, physics, and computational sciences, where high-fidelity models (often governed by differential equations and involving a large number of variables or degrees of freedom) can be computationally expensive to simulate and analyze.

A Newton fractal is a type of fractal generated using Newton's method for finding successively better approximations to the roots (or zeros) of a complex polynomial function. The process involves iterating the Newton-Raphson formula, which is a method for finding roots of a real-valued function. In the context of complex analysis, this method can be visualized in the complex plane, leading to the creation of intricate and visually appealing fractal patterns.

Proper Generalized Decomposition (PGD) is a mathematical and numerical approach used to solve complex, high-dimensional problems, particularly in the field of computational mathematics and engineering. This method is especially useful for problems governed by partial differential equations (PDEs), which can be computationally intensive to solve directly, particularly when dealing with large-scale systems or when high-dimensional parameter spaces are involved.

Quantification of Margins and Uncertainties (QMU) is a systematic approach used typically in engineering, particularly in the fields of aerospace, nuclear, and other complex systems, to assess and manage the uncertainties and margins in performance predictions of a system. The objective of QMU is to provide a comprehensive understanding of how uncertainties in various inputs and parameters affect the performance and reliability of a system.

Runge–Kutta methods are a family of iterative techniques used for solving ordinary differential equations (ODEs). These methods are employed to find numerical approximations to the solutions of initial value problems, where the goal is to compute the future values of a function given its current state and the rate of change defined by the differential equation. The most commonly used member of this family is the classical fourth-order Runge-Kutta method, often abbreviated as RK4.

Sinc numerical methods are computational techniques that utilize the Sinc function, which is defined as: \[ \text{sinc}(x) = \begin{cases} \frac{\sin(\pi x)}{\pi x} & \text{if } x \neq 0 \\ 1 & \text{if } x = 0 \end{cases} \] Sinc methods are often used in various areas of numerical analysis, particularly in interpolation, numerical integration, and

Negamax is a simplified version of the minimax algorithm, used in two-player zero-sum games such as chess, checkers, and tic-tac-toe. It is a decision-making algorithm that enables players to choose the optimal move by minimizing their opponent's maximum possible score while maximizing their own score. The core idea behind Negamax is based on the principle that if one player's gain is the other player's loss, the two can be treated symmetrically.

A **sparse grid** is a mathematical and computational technique used primarily in numerical analysis and approximation theory to efficiently represent high-dimensional functions or data. Sparse grids are particularly useful in scenarios where dealing with full grid representations is computationally expensive or infeasible due to the "curse of dimensionality." ### Key Concepts: 1. **Grid Representation**: In high-dimensional spaces, a full grid would require evaluating a function at every combination of points in each dimension.

The field of numerical analysis has evolved significantly since 1945, with many key developments, algorithms, and theories emerging over the decades. Below is a timeline highlighting important events and milestones in numerical analysis from 1945 onward: ### 1940s - **1945**: The establishment of modern numerical analysis begins as computers emerge. Early work focuses on basic algorithms for arithmetic operations and solving linear equations.

The truncated power function is a mathematical function that is often used in various fields such as economics, statistics, and machine learning.

Vector field reconstruction refers to the process of estimating a vector field from a set of discrete data points or measurements. A vector field is a representation of a vector quantity (which has both magnitude and direction) at different points in space. Common applications include fluid dynamics, electromagnetism, and computer graphics.

A well-posed problem is a concept from mathematics, particularly in the context of mathematical analysis and the theory of partial differential equations. The term is typically attributed to the French mathematician Jacques Hadamard, who outlined specific criteria for a problem to be considered well-posed. According to Hadamard, a problem is well-posed if it satisfies the following three conditions: 1. **Existence**: There is at least one solution to the problem.

The K-server problem is a well-known problem in the field of online algorithms and competitive analysis. It involves managing the movements of a number of servers (typically represented as points on a metric space) to serve requests that arrive over time. The primary objective is to minimize the total distance traveled by the servers while responding to these requests.

Backtracking line search is an optimization technique used to determine an appropriate step size for iterative algorithms, particularly in the context of gradient-based optimization methods. The goal of the line search is to find a step size that will sufficiently decrease the objective function while ensuring that the search doesn't jump too far, which could potentially lead to instability or divergence.

A Guillotine partition refers to a method of dividing a geometric space, commonly used in computational geometry, optimization, and various applications such as packing problems and resource allocation. The term is often associated with the partitioning of a rectangular area into smaller rectangles using a series of straight cuts, resembling the action of a guillotine. In a Guillotine partition, the cuts are made either vertically or horizontally, and each cut subdivides the current region into two smaller rectangles.