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.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
KlystronA klystron is a specialized linear-beam vacuum tube, invented in 1937 by American electrical engineers Russell and Sigurd Varian, which is used as an amplifier for high radio frequencies, from UHF up into the microwave range. Low-power klystrons are used as oscillators in terrestrial microwave relay communications links, while high-power klystrons are used as output tubes in UHF television transmitters, satellite communication, radar transmitters, and to generate the drive power for modern particle accelerators.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
GyrotronA gyrotron is a class of high-power linear-beam vacuum tubes that generates millimeter-wave electromagnetic waves by the cyclotron resonance of electrons in a strong magnetic field. Output frequencies range from about 20 to 527 GHz, covering wavelengths from microwave to the edge of the terahertz gap. Typical output powers range from tens of kilowatts to 1–2 megawatts. Gyrotrons can be designed for pulsed or continuous operation. The gyrotron was invented by Soviet scientists at NIRFI, based in Nizhny Novgorod, Russia.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Vacuum tubeA vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied. The type known as a thermionic tube or thermionic valve utilizes thermionic emission of electrons from a hot cathode for fundamental electronic functions such as signal amplification and current rectification.
Electronic oscillatorAn electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found in many electronic devices, such as radio receivers, television sets, radio and television broadcast transmitters, computers, computer peripherals, cellphones, radar, and many other devices.
Multi-configurational self-consistent fieldMulti-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule.
Electron-beam lithographyElectron-beam lithography (often abbreviated as e-beam lithography, EBL) is the practice of scanning a focused beam of electrons to draw custom shapes on a surface covered with an electron-sensitive film called a resist (exposing). The electron beam changes the solubility of the resist, enabling selective removal of either the exposed or non-exposed regions of the resist by immersing it in a solvent (developing). The purpose, as with photolithography, is to create very small structures in the resist that can subsequently be transferred to the substrate material, often by etching.
Parasitic oscillationParasitic oscillation is an undesirable electronic oscillation (cyclic variation in output voltage or current) in an electronic or digital device. It is often caused by feedback in an amplifying device. The problem occurs notably in RF, audio, and other electronic amplifiers as well as in digital signal processing. It is one of the fundamental issues addressed by control theory. Parasitic oscillation is undesirable for several reasons. The oscillations may be coupled into other circuits or radiate as radio waves, causing electromagnetic interference (EMI) to other devices.
Electrical connectorComponents of an electrical circuit are electrically connected if an electric current can run between them through an electrical conductor. An electrical connector is an electromechanical device used to create an electrical connection between parts of an electrical circuit, or between different electrical circuits, thereby joining them into a larger circuit. Most electrical connectors have a gender - i.e. the male component, called a plug, connects to the female component, or socket.
Electron gunAn electron gun (also called electron emitter) is an electrical component in some vacuum tubes that produces a narrow, collimated electron beam that has a precise kinetic energy. The largest use is in cathode-ray tubes (CRTs), used in older television sets, computer displays and oscilloscopes, before the advent of flat-panel displays. Electron guns are also used in field-emission displays (FEDs), which are essentially flat-panel displays made out of rows of extremely small cathode-ray tubes.
ElectronThe electron (_Electron or _beta-) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ.
Parasitic capacitanceParasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages are close together, the electric field between them causes electric charge to be stored on them; this effect is capacitance. All practical circuit elements such as inductors, diodes, and transistors have internal capacitance, which can cause their behavior to depart from that of ideal circuit elements.
Cathode rayCathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to electrons emitted from the cathode (the electrode connected to the negative terminal of the voltage supply). They were first observed in 1859 by German physicist Julius Plücker and Johann Wilhelm Hittorf, and were named in 1876 by Eugen Goldstein Kathodenstrahlen, or cathode rays.
