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Propagation of a ray through a layer. The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films.
An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.
Bairstow's approach is to use Newton's method to adjust the coefficients u and v in the quadratic + + until its roots are also roots of the polynomial being solved. The roots of the quadratic may then be determined, and the polynomial may be divided by the quadratic to eliminate those roots.
Finding roots in a specific region of the complex plane, typically the real roots or the real roots in a given interval (for example, when roots represents a physical quantity, only the real positive ones are interesting). For finding one root, Newton's method and other general iterative methods work generally well.
Active absorption refers to the absorption of water by roots with the help of adenosine triphosphate, generated by the root respiration: as the root cells actively take part in the process, it is called active absorption. According to Jenner, active absorption takes place in low transpiring and well-watered plants, and 4% of total water ...
As one example, if there is free space between the two planes, the ray transfer matrix is given by: = [], where d is the separation distance (measured along the optical axis) between the two reference planes.
In plants and animals, mineral absorption, also called mineral uptake is the way in which minerals enter the cellular material, typically following the same pathway as water. In plants, the entrance portal for mineral uptake is usually through the roots. Some mineral ions diffuse in-between the cells. In contrast to water, some minerals are ...
b k is the current iterate, i.e., the current guess for the root of f. a k is the "contrapoint," i.e., a point such that f(a k) and f(b k) have opposite signs, so the interval [a k, b k] contains the solution. Furthermore, |f(b k)| should be less than or equal to |f(a k)|, so that b k is a better guess for the unknown solution than a k.