Numerical analysis is the study of algorithms for the problems of continuous mathematics. It develops methods that obtain approximate solutions within controlled, known error bounds for problems that are impractical or impossible to solve exactly by symbolic methods. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Central QuestionHow can a problem of continuous mathematics be solved by an algorithm that produces an approximate answer within a controlled, known error bound? 1 Key DebateA central working tension in the field is controlling how errors compound during a calculation: an algorithm is called numerically stable only if an error, whatever its cause, does not grow to be much larger as the calculation proceeds, which drives much of the field's method design. 1 Classification
Pure or Applied Numerical Analysis
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Source Numerical Analysis (Wikipedia)
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Source Abraham Sharp (Wikipedia)
Source MacTutor biography of Alston Householder, St Andrews
Source Arima Yoriyuki (Wikipedia)
Source Bernstein Polynomial (Wikipedia)
Source Bulgarian Academy of Sciences: 90 years since the birth of Acad. Blagovest Sendov (1932-2020)
Source Carl Runge, Biography (MacTutor History of Mathematics)
Source Charles George Broyden (Wikipedia)
Source Condition Number (Wikipedia)
Source Donald Goldfarb (Wikipedia)
Source Douglas Hartree (Wikipedia)
Source E. T. Whittaker (Wikipedia)
Source Eduard Stiefel (Wikipedia)
Source Friedrich L. Bauer (Wikipedia)
Source George Pólya (Wikipedia)
Source John Crank (Wikipedia)
Source Joseph Raphson (MacTutor)
Source Lewis Fry Richardson (Wikipedia)
Source Martin Kutta, Biography (MacTutor History of Mathematics)
Source Michel Crouzeix (Mathematics Genealogy Project)
Source Olga Ladyzhenskaya (Wikipedia)
Source Philipp Ludwig von Seidel (Wikipedia)
Source Phyllis Nicolson (Wikipedia)
Source Roger Cotes (Wikipedia)
Source MacTutor History of Mathematics: Semyon Gershgorin
Source Thomas Simpson (MacTutor)
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1. Numerical Analysis (Wikipedia)
Wikimedia Foundationlead paragraph
Numerical analysis is the study of algorithms for the problems of continuous mathematics.
body text
rather than giving exact symbolic answers translated into digits and applicable only to real-world measurements, approximate solutions within specified error bounds are used
body text on stability
An algorithm is called numerically stable if an error, whatever its cause, does not grow to be much larger during the calculation.
Applications section
Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.
View the Source Michel Crouzeix (Mathematics Genealogy Project)
Includes: Michel Crouzeix, Degree recordQuote, Includes: Michel Crouzeix, Degree record
Numerical analysis
MacTutor History of Mathematics: Semyon Gershgorin
Includes: Semyon Aranovich Gershgorin, Biography textQuote, Includes: Semyon Aranovich Gershgorin, Biography text
Semyon Gershgorin was a Belarussian mathematician who produced important results in numerical approximation
Joseph Raphson (MacTutor)
Includes: Joseph Raphson, SummaryQuote, Includes: Joseph Raphson, Summary
Joseph Raphson was an English mathematician credited with the independent discovery of Newton's method for solving equations numerically.
Bulgarian Academy of Sciences: 90 years since the birth of Acad. Blagovest Sendov (1932-2020)
Bulgarian Academy of SciencesIncludes: Blagovest Sendov, Scientific interestsQuote, Includes: Blagovest Sendov, Scientific interests
The scientific interests and achievements of Acad. Sendov are in the field of approximation theory, mathematical modelling (in particular in mathematical biology), numerical methods and computer science
E. T. Whittaker (Wikipedia)
Includes: Edmund Taylor Whittaker, LeadQuote, Includes: Edmund Taylor Whittaker, Lead
renowned for his research in mathematical physics and numerical analysis
Friedrich L. Bauer (Wikipedia)
Includes: Friedrich L. Bauer, Work, numerical analysisQuote, Includes: Friedrich L. Bauer, Work, numerical analysis
His scientific contributions spread from numerical analysis (Bauer-Fike theorem)
John Crank (Wikipedia)
Includes: John Crank, Biography, field of workQuote, Includes: John Crank, Biography, field of work
best known for his work on the numerical solution of partial differential equations
Phyllis Nicolson (Wikipedia)
Includes: Phyllis Nicolson, Hartree Differential Analyser workQuote, Includes: Phyllis Nicolson, Hartree Differential Analyser work
Nicolson became a proficient numerical analyst
Charles George Broyden (Wikipedia)
Includes: Charles George Broyden, LeadQuote, Includes: Charles George Broyden, Lead
specialized in optimization problems and numerical linear algebra
Donald Goldfarb (Wikipedia)
Includes: Donald Goldfarb, Lead, numerical analysisQuote, Includes: Donald Goldfarb, Lead, numerical analysis
best known for his works in mathematical optimization and numerical analysis
Lewis Fry Richardson (Wikipedia)
Includes: Lewis Fry Richardson, LeadQuote, Includes: Lewis Fry Richardson, Lead
a method for solving a system of linear equations known as modified Richardson iteration
Douglas Hartree (Wikipedia)
Includes: Douglas Hartree, LeadQuote, Includes: Douglas Hartree, Lead
most famous for the development of numerical analysis
Philipp Ludwig von Seidel (Wikipedia)
Includes: Philipp Ludwig von Seidel, LeadQuote, Includes: Philipp Ludwig von Seidel, Lead
The Gauss-Seidel method is a useful numerical iterative method for solving linear systems.
Olga Ladyzhenskaya (Wikipedia)
Includes: Olga Ladyzhenskaya, Mathematical accomplishmentsQuote, Includes: Olga Ladyzhenskaya, Mathematical accomplishments
She provided the first rigorous proofs of the convergence of a finite difference method
Eduard Stiefel (Wikipedia)
Includes: Eduard Stiefel, Career, numerical mathematicsQuote, Includes: Eduard Stiefel, Career, numerical mathematics
He later turned entirely to numerical mathematics.
Abraham Sharp (Wikipedia)
Includes: Abraham Sharp, Lead, field of workQuote, Includes: Abraham Sharp, Lead, field of work
Sharp calculated pi to 72 decimal places using an arctan sequence, briefly holding the record until John Machin calculated 100 digits in 1706.
Arima Yoriyuki (Wikipedia)
Includes: Arima Yoriyuki, LeadQuote, Includes: Arima Yoriyuki, Lead
rational approximation of
Roger Cotes (Wikipedia)
Includes: Roger Cotes, Lead, field of workQuote, Includes: Roger Cotes, Lead, field of work
He also devised the quadrature formulas known as Newton-Cotes formulas, which originated from Newton's research, and made a geometric argument that can be interpreted as a logarithmic version of Euler's formula.
Thomas Simpson (MacTutor)
Includes: Thomas Simpson, Summary and biographyQuote, Includes: Thomas Simpson, Summary and biography
Thomas Simpson was an English mathematician who is best remembered for his work on interpolation and numerical methods of integration.
Bernstein Polynomial (Wikipedia)
Includes: Bernstein Polynomial, Lead sentenceQuote, Includes: Bernstein Polynomial, Lead sentence
In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Berns
Condition Number (Wikipedia)
Includes: Condition Number, Lead sentenceQuote, Includes: Condition Number, Lead sentence
In numerical analysis, the condition number of a function measures how much the output value of the function can change for a smal
George Pólya (Wikipedia)
Includes: George Pólya, Lead paragraph [in-branch 4]Quote, Includes: George Pólya, Lead paragraph [in-branch 4]
numerical analysis
MacTutor biography of Alston Householder, St Andrews
Includes: Alston Householder, SummaryQuote, Includes: Alston Householder, Summary
Alston Householder was an American mathematician who worked in mathematical biology and numerical analysis.
Carl Runge, Biography (MacTutor History of Mathematics)
Includes: Carl Runge, SummaryQuote, Includes: Carl Runge, Summary
Carl Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements.
Martin Kutta, Biography (MacTutor History of Mathematics)
Includes: Martin Kutta, SummaryQuote, Includes: Martin Kutta, Summary
Wilhelm Kutta was a German engineer who is best known for his work on the numerical solution of differential equations ( the Runge-Kutta method ) .
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