Ask the ChatbotGames & QuizzesHistory & SocietyScience & TechBiographiesAnimals & NatureGeography & TravelArts & CultureProConMoneyVideos
regularization
Directory
References
Discover
Space race (1957-1969) infographic between United States (U.S.) and Russia. America, Soviet Union, U.S.S.R., space exploration
Timeline of the Space Race, 1957–69
Shadow of a man holding large knife in his hand inside of some dark, spooky buiding
7 of History's Most Notorious Serial Killers
Ahura Mazda - relief of the Zoroastrian god Ahura Mazda at the ancient ruins of Persepolis in Iran. Also known as Ormazd Zoroastrianism,
Which Religion Is the Oldest?
Groups of depositors in front of the closed American Union Bank, New York City. April 26, 1932. Great Depression run on bank crowd
Causes of the Great Depression
Scolex (head) of the tapeworm Taenia solium. The hooks of the scolex enable the tapeworm to attach to the intestinal wall.
Uninvited Guests: The 7 Worst Parasitic Worms
VAN, TURKEY - OCTOBER 25: A building and car ruined during the earthquake of Van-Ercis on October 25, 2011 in Van, Turkey. It is 604 killed and 4152 injured in Van-Ercis Earthquake.
What Is an Aftershock?
Korean War - U.S. Marines watch explosions of bombs dropped by Marine Vought F4U Corsair fighter bomber planes during the Battle of Chosin Reservoir, Korea, in December 1950. soldiers
Korean War Timeline

regularization

mathematics
Also known as: smoothing

Learn about this topic in these articles:

celestial mechanics

  • geocentric system
    In celestial mechanics: Numerical solutions

    In this process, called regularization, the encounter is traversed in less computer time while preserving reasonable accuracy. This process is impractical when n is large, so accelerations are usually artificially bounded on close approaches to prevent instabilities in the numerical calculation and to prevent slowing the calculation. For example,…

    Read More
Britannica Chatbot logo

Britannica Chatbot

Chatbot answers are created from Britannica articles using AI. This is a beta feature. AI answers may contain errors. Please verify important information using Britannica articles. About Britannica AI.
functional analysis
Table of Contents
Introduction References & Edit History Quick Facts & Related Topics
Quizzes
Equations written on blackboard
Numbers and Mathematics
Discover
Gills of three old specimens of webcap fungus (Cortinarius) in Gloucestershire, South West England. toxic, fungi, poisonous mushroom
7 of the World’s Most Poisonous Mushrooms
VAN, TURKEY - OCTOBER 25: A building and car ruined during the earthquake of Van-Ercis on October 25, 2011 in Van, Turkey. It is 604 killed and 4152 injured in Van-Ercis Earthquake.
What Is an Aftershock?
Vietnam War. U.S. President Lyndon B. Johnson awards the Distinguished Service Cross to First Lieutenant Marty A. Hammer, during a visit to military personnel, Cam Ranh Bay, South Vietnam, October 26, 1966. President Johnson
Vietnam War Timeline
earthquake. Heavily damaged school in the town of Yingxiu after a major earthquake struck China's Sichuan Province on May 12, 2008.
The 6 Deadliest Earthquakes Since 1950
African Americans demonstrating for voting rights in front of the White House as police and others watch, March 12, 1965. One sign reads, "We demand the right to vote everywhere." Voting Rights Act, civil rights.
Timeline of the American Civil Rights Movement
World Data Locator Map: Australia
Is Australia an Island?
A mug shot taken by the regional Colombia control agency in Medellin
Pablo Escobar: 8 Interesting Facts About the King of Cocaine

functional analysis

mathematics
External Websites
Also known as: function analysis
Written and fact-checked by
The Editors of Encyclopaedia Britannica
Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors.
The Editors of Encyclopaedia Britannica
Article History

functional analysis, Branch of mathematical analysis dealing with functionals, or functions of functions. It emerged as a distinct field in the 20th century, when it was realized that diverse mathematical processes, from arithmetic to calculus procedures, exhibit very similar properties. A functional, like a function, is a relationship between objects, but the objects may be numbers, vectors, or functions. Groupings of such objects are called spaces. Differentiation is an example of a functional because it defines a relationship between a function and another function (its derivative). Integration is also a functional. Functional analysis focuses on classes of functions, such as those that can be differentiated or integrated.

This article was most recently revised and updated by William L. Hosch.
Britannica Chatbot logo

Britannica Chatbot

Chatbot answers are created from Britannica articles using AI. This is a beta feature. AI answers may contain errors. Please verify important information using Britannica articles. About Britannica AI.