Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Biconjugate gradient methodIn mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations Unlike the conjugate gradient method, this algorithm does not require the matrix to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose A*. Choose initial guess , two other vectors and and a preconditioner for do In the above formulation, the computed and satisfy and thus are the respective residuals corresponding to and , as approximate solutions to the systems is the adjoint, and is the complex conjugate.
Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
Classical central-force problemIn classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field. A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. In a few important cases, the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions.
Systems scienceSystems science, also referred to as systems research, or, simply, systems, is a transdisciplinary field concerned with understanding systems—from simple to complex—in nature, society, cognition, engineering, technology and science itself. The field is diverse, spanning the formal, natural, social, and applied sciences. To systems scientists, the world can be understood as a system of systems.
Steffensen's methodIn numerical analysis, Steffensen's method is an iterative method for root-finding named after Johan Frederik Steffensen which is similar to Newton's method, but with certain situational advantages. In particular, Steffensen's method achieves similar quadratic convergence, but without using derivatives as Newton's method does.
Mira variableMira variables ˈmaɪrə (named for the prototype star Mira) are a class of pulsating stars characterized by very red colours, pulsation periods longer than 100 days, and amplitudes greater than one magnitude in infrared and 2.5 magnitude at visual wavelengths. They are red giants in the very late stages of stellar evolution, on the asymptotic giant branch (AGB), that will expel their outer envelopes as planetary nebulae and become white dwarfs within a few million years.
Systems engineeringSystems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge. The individual outcome of such efforts, an engineered system, can be defined as a combination of components that work in synergy to collectively perform a useful function.
Trip distributionTrip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route assignment) in the traditional four-step transportation forecasting model. This step matches tripmakers’ origins and destinations to develop a “trip table”, a matrix that displays the number of trips going from each origin to each destination. Historically, this component has been the least developed component of the transportation planning model.
Classical mechanicsClassical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The "classical" in "classical mechanics" does not refer classical antiquity, as it might in, say, classical architecture.
