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).
Superposition principleThe superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y). A function that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity and homogeneity for scalar a.
Root mean squareIn mathematics and its applications, the root mean square of a set of numbers (abbreviated as RMS, or rms and denoted in formulas as either or ) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted ) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted ) can be defined in terms of an integral of the squares of the instantaneous values during a cycle.
Armature (electrical)In electrical engineering, the armature is the winding (or set of windings) of an electric machine which carries alternating current. The armature windings conduct AC even on DC machines, due to the commutator action (which periodically reverses current direction) or due to electronic commutation, as in brushless DC motors. The armature can be on either the rotor (rotating part) or the stator (stationary part), depending on the type of electric machine.
Magnetic amplifierThe magnetic amplifier (colloquially known as a "mag amp") is an electromagnetic device for amplifying electrical signals. The magnetic amplifier was invented early in the 20th century, and was used as an alternative to vacuum tube amplifiers where robustness and high current capacity were required. World War II Germany perfected this type of amplifier, and it was used in the V-2 rocket. The magnetic amplifier was most prominent in power control and low-frequency signal applications from 1947 to about 1957, when the transistor began to supplant it.
Choke (electronics)In electronics, a choke is an inductor used to block higher-frequency alternating currents (AC) while passing direct current (DC) and lower-frequency ACs in a circuit. A choke usually consists of a coil of insulated wire often wound on a magnetic core, although some consist of a doughnut-shaped ferrite bead strung on a wire. The choke's impedance increases with frequency. Its low electrical resistance passes both AC and DC with little power loss, but its reactance limits the amount of AC passed.
Damper (flow)A damper is a valve or plate that stops or regulates the flow of air inside a duct, chimney, VAV box, air handler, or other air-handling equipment. A damper may be used to cut off central air conditioning (heating or cooling) to an unused room, or to regulate it for room-by-room temperature and climate control -- for example in the case of Volume Control Dampers. Its operation can be manual or automatic. Manual dampers are turned by a handle on the outside of a duct.
Enigma machineThe Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the German military. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages. The Enigma has an electromechanical rotor mechanism that scrambles the 26 letters of the alphabet.
Torsion bar suspensionA torsion bar suspension, also known as a torsion spring suspension, is any vehicle suspension that uses a torsion bar as its main weight-bearing spring. One end of a long metal bar is attached firmly to the vehicle chassis; the opposite end terminates in a lever, the torsion key, mounted perpendicular to the bar, that is attached to a suspension arm, a spindle, or the axle. Vertical motion of the wheel causes the bar to twist around its axis and is resisted by the bar's torsion resistance.
Diesel multiple unitA diesel multiple unit or DMU is a multiple-unit train powered by on-board diesel engines. A DMU requires no separate locomotive, as the engines are incorporated into one or more of the carriages. Diesel-powered single-unit railcars are also generally classed as DMUs. Diesel-powered units may be further classified by their transmission type: diesel–mechanical DMMU, diesel–hydraulic DHMU, or diesel–electric DEMU. The diesel engine may be located above the frame in an engine bay or under the floor.
