Root-mean-square deviationThe root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. These deviations are called residuals when the calculations are performed over the data sample that was used for estimation and are called errors (or prediction errors) when computed out-of-sample.
Star clusterStar clusters are large groups of stars held together by self-gravitation. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clustered groups of stars, generally containing fewer than a few hundred members, and are often very young.
Dwarf galaxyA dwarf galaxy is a small galaxy composed of about 1000 up to several billion stars, as compared to the Milky Way's 200–400 billion stars. The Large Magellanic Cloud, which closely orbits the Milky Way and contains over 30 billion stars, is sometimes classified as a dwarf galaxy; others consider it a full-fledged galaxy. Dwarf galaxies' formation and activity are thought to be heavily influenced by interactions with larger galaxies. Astronomers identify numerous types of dwarf galaxies, based on their shape and composition.
Timeline of knowledge about galaxies, clusters of galaxies, and large-scale structureThe following is a timeline of galaxies, clusters of galaxies, and large-scale structure of the universe. 5th century BC — Democritus proposes that the bright band in the night sky known as the Milky Way might consist of stars. 4th century BC — Aristotle believes the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together" and that the "ignition takes place in the upper part of the atmosphere, in the region of the world which is continuous with the heavenly motions".
Observable universeThe observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons.
Elliptical galaxyAn elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the four main classes of galaxy described by Edwin Hubble in his Hubble sequence and 1936 work The Realm of the Nebulae, along with spiral and lenticular galaxies. Elliptical (E) galaxies are, together with lenticular galaxies (S0) with their large-scale disks, and ES galaxies with their intermediate scale disks, a subset of the "early-type" galaxy population.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Least squaresThe method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Reduced chi-squared statisticIn statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) It is defined as chi-square per degree of freedom: where the chi-squared is a weighted sum of squared deviations: with inputs: variance , observations O, and calculated data C.
