Round-off errorIn computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Truncation errorIn numerical analysis and scientific computing, truncation error is an error caused by approximating a mathematical process. A summation series for is given by an infinite series such as In reality, we can only use a finite number of these terms as it would take an infinite amount of computational time to make use of all of them. So let's suppose we use only three terms of the series, then In this case, the truncation error is Example A: Given the following infinite series, find the truncation error for x = 0.
Modular arithmeticIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.
PaperPaper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses, or other vegetable sources in water, draining the water through a fine mesh leaving the fibre evenly distributed on the surface, followed by pressing and drying. Although paper was originally made in single sheets by hand, almost all is now made on large machines—some making reels 10 metres wide, running at 2,000 metres per minute and up to 600,000 tonnes a year.
Lyapunov functionIn the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.
Aluminum electrolytic capacitorAluminum electrolytic capacitors are polarized electrolytic capacitors whose anode electrode (+) is made of a pure aluminum foil with an etched surface. The aluminum forms a very thin insulating layer of aluminum oxide by anodization that acts as the dielectric of the capacitor. A non-solid electrolyte covers the rough surface of the oxide layer, serving in principle as the second electrode (cathode) (-) of the capacitor. A second aluminum foil called “cathode foil” contacts the electrolyte and serves as the electrical connection to the negative terminal of the capacitor.
BiasBias is a disproportionate weight in favor of or against an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, or a belief. In science and engineering, a bias is a systematic error. Statistical bias results from an unfair sampling of a population, or from an estimation process that does not give accurate results on average. The word appears to derive from Old Provençal into Old French biais, "sideways, askance, against the grain".
Polymer capacitorA polymer capacitor, or more accurately a polymer electrolytic capacitor, is an electrolytic capacitor (e-cap) with a solid conductive polymer electrolyte. There are four different types: Polymer tantalum electrolytic capacitor (Polymer Ta-e-cap) Polymer aluminium electrolytic capacitor (Polymer Al-e-cap) Hybrid polymer capacitor (Hybrid polymer Al-e-cap) Polymer niobium electrolytic capacitors Polymer Ta-e-caps are available in rectangular surface-mounted device (SMD) chip style.
EstimatorIn statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.
