Backward Forward Error
Contents |
by introducing more precise citations. (February 2012) (Learn how and when to remove this template message) In the mathematical subfield of numerical analysis, numerical stability forward and backward error correction is a generally desirable property of numerical algorithms. The precise definition of
Forward And Backward Error Recovery
stability depends on the context. One is numerical linear algebra and the other is algorithms for solving backward error analysis example 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
Stability Of Numerical Methods
nearly colliding eigenvalues. On the other hand, in numerical algorithms for differential equations the concern is the growth of round-off errors and/or initially small fluctuations in initial data which might cause a large deviation of final answer from the exact solution. Some numerical algorithms may damp out the small fluctuations (errors) in the input data; others might magnify such backward stability errors. Calculations that can be proven not to magnify approximation errors are called numerically stable. One of the common tasks of numerical analysis is to try to select algorithms which are robust– that is to say, do not produce a wildly different result for very small change in the input data. An opposite phenomenon is instability. Typically, an algorithm involves an approximate method, and in some cases one could prove that the algorithm would approach the right solution in some limit. Even in this case, there is no guarantee that it would converge to the correct solution, because the floating-point round-off or truncation errors can be magnified, instead of damped, causing the deviation from the exact solution to grow exponentially.[1] Contents 1 Stability in numerical linear algebra 2 Stability in numerical differential equations 3 See also 4 References Stability in numerical linear algebra[edit] There are different ways to formalize the concept of stability. The following definitions of forward, backward, and mixed stability are often used in numerical linear algebra. Diagram showing the forward error Δy
View all reference sources FREE REFERENCE ENTRIES A B C D E F G H I J K L M N O P Q R
Numerical Stability Example
S T U V W X Y Z # Home Dictionaries,
Numerical Stability Of Algorithms
Thesauruses, Pictures, and Press Releases A Dictionary of Computing January 2004 backward error correction Print this article Cite numerical instability example this article Tools A Dictionary of Computing | 2004 | 700+ words © A Dictionary of Computing 2004, originally published by Oxford University Press 2004. backward error correction https://en.wikipedia.org/wiki/Numerical_stability (backward correction) Error correction that occurs in a channel through the detection of errors by the receiver: the receiver responds to any errors in a block by requesting the transmitter to retransmit the affected block. Backward correction requires a return channel, by contrast with forward error correction.There are two ways in which the return channel can be used http://www.encyclopedia.com/doc/1O11-backwarderrorcorrection.html to indicate errors: positive acknowledgment and negative acknowledgment. With positive acknowledgment, the receiver returns confirmation of each block received correctly, and the transmitter is prepared to retransmit a block that is not acknowledged within an appropriate time. With negative acknowledgment, the receiver returns a request to retransmit any block received erroneously, and the transmitter is prepared to retransmit such a block (implying that the transmitter retains a copy of every block sent, indefinitely).Since the return channel itself may be prone to errors, and to limit the amount of storage necessary at the transmitter, the positive acknowledgment and retransmission (PAR) technique is generally preferred. See also error-detecting code. Cite this article Pick a style below, and copy the text for your bibliography. MLA Chicago APA JOHN DAINTITH. "backward error correction." A Dictionary of Computing. 2004. Encyclopedia.com. 1 Oct. 2016
re-send information. Backward Error Correction is used in situations where some of the transmitted data has been lost or corrupted during transit and the http://www.tech-faq.com/backward-error-correction-bec.html transmitting device must resend the information in order for the receiving device to understand the transmission. Backward Error Correction is the opposite of “Forward Error Correction”, in which a transmitting device simply sends redundant information to make up for any potential errors. How Backward Error Correction Works Backward Error Correction is dependent on a number of protocols and backward error algorithms, such as parity bits, cyclic redundancy checks, and longitudinal redundancy checks, but relies on the same procedure. As usual, a transmitting device will send data to a receiving device. The receiving device will then run checks to ensure that all of the information is present, readable, and makes sense. If the received information does not make sense, is not forward and backward all there, or cannot be read for any reason, the receiving device will send a request to the transmitting device to resend that data. Applications Backward Error Correction is often used instead of Forward Error Correction because it requires less bandwidth. However, because Backward Error Correction requires the receiving device to receive a signal before it requests redundant information, it requires more time than Forward Error Correction and may even use more bandwidth for individual transfers due to constant messaging between the two devices. While Forward Error Correction is usually preferred on systems that are prone to errors, such as long-distance communications systems, Backward Error Correction is ideal for systems that rarely have errors or only handle small amounts of data. Follow Us! Rate this article: ★ ★ ★ ★ ★ Backward Error Correction (BEC), 4.67 / 5 (3 votes) You need to enable JavaScript to vote Mail this article Print this article Last updated 11 March, 2016. Related Posts Satellite Systems The basic types of satellite systems include geostationary (GEO), Low Earth Orbit (LEO), Mediu
be down. Please try the request again. Your cache administrator is webmaster. Generated Sat, 01 Oct 2016 22:46:33 GMT by s_hv1002 (squid/3.5.20)