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.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.
Fixed-point arithmeticIn computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals.
Error analysis (mathematics)In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics. In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean. For instance, in a system modeled as a function of two variables Error analysis deals with the propagation of the numerical errors in and (around mean values and ) to error in (around a mean ).
Catastrophic cancellationIn numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one long and the other long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be and . These may be good approximations, in relative error, to the true lengths: the approximations are in error by less than 2% of the true lengths, .
Digital signal processingDigital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
Software licenseA software license is a legal instrument (usually by way of contract law, with or without printed material) governing the use or redistribution of software. Under United States copyright law, all software is copyright protected, in both source code and object code forms, unless that software was developed by the United States Government, in which case it cannot be copyrighted. Authors of copyrighted software can donate their software to the public domain, in which case it is also not covered by copyright and, as a result, cannot be licensed.
Quadruple-precision floating-point formatIn computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables.
Accuracy and precisionAccuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other. In other words, precision is a description of random errors, a measure of statistical variability. Accuracy has two definitions: More commonly, it is a description of only systematic errors, a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this trueness.
