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Quadratic programming. Quadratic programming ( QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.
Analytic reasoning. Analytical reasoning, also known as analytical thinking, [1] refers to the ability to look at information, be it qualitative or quantitative in nature, and discern patterns within the information. Analytical reasoning involves breaking down large problems into smaller components [2] and using deductive reasoning with no ...
Initial value problem. In multivariable calculus, an initial value problem [a] ( IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.
Sod shock tube. The Sod shock tube problem, named after Gary A. Sod, is a common test for the accuracy of computational fluid codes, like Riemann solvers, and was heavily investigated by Sod in 1978. The test consists of a one-dimensional Riemann problem with the following parameters, for left and right states of an ideal gas .
One does not use critical thinking to solve problems—one uses critical thinking to improve one's process of thinking. "An appraisal based on careful analytical evaluation" "Critical thinking is a type of thinking pattern that requires people to be reflective, and pay attention to decision-making which guides their beliefs and actions.
The homotopy analysis method ( HAM) is a semi-analytical technique to solve nonlinear ordinary / partial differential equations. The homotopy analysis method employs the concept of the homotopy from topology to generate a convergent series solution for nonlinear systems. This is enabled by utilizing a homotopy- Maclaurin series to deal with the ...
A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution . In mathematics, conventional optimization problems are usually stated in terms of minimization. A local minimum x* is defined as an element for which there exists some δ > 0 such that.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case.