Arithmetic | Numerical analysis | Data types | Computer arithmetic
Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities. For example, instead of saying the height of someone is approximately 2 meters, one could using interval arithmetic, say that the height of the person is definitely between 1.97 meters and 2.03 meters. Mathematically, using interval arithmetic, instead of working with an uncertain real-valued variable , one works with an interval that defines the range of values that can have. In other words, any value of the variable lies in the closed interval between and . A function , when applied to , yields an inexact value; instead produces an interval which includes all the possible values for for all . Interval arithmetic is suitable for a variety of purposes; the most common use is in scientific works, particularly when the calculations are handled by software, where it is used to keep track of rounding errors in calculations and of uncertainties in the knowledge of the exact values of physical and technical parameters. The latter often arise from measurement errors and tolerances for components or due to limits on computational accuracy. Interval arithmetic also helps find guaranteed solutions to equations (such as differential equations) and optimization problems. (Wikipedia).
Measurement, approximation and interval arithmetic (I) | Real numbers and limits Math Foundations 81
This video introduces interval arithmetic, first in the context of natural numbers, and then for integers. We start with some remarks from the previous video on the difficulties with irrational numbers, sqrt(2), pi and e. Then we give some general results about order (less than, greater
From playlist Math Foundations
Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82
We continue on with a short intro to interval arithmetic, noting the difference between the laws of arithmetic over the natural numbers and the integers. The case of rational number intervals is also briefly discussed. We end the lecture with some remarks on the vagueness of ``real number'
From playlist Math Foundations
Interval Notation (What is It?)
Interval Notation Versus Inequality Notation. Learn the difference in this video by Mario's Math Tutoring. We discuss the difference between a closed interval and an open interval. Also we discuss how infinity works with interval notation. Interval Notation is often used when writing the
From playlist Algebra 2
Using Clocks to Solve Fractions String 8
A fun string dealing with subtraction that leads to sixths and twelfths
From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents
Interval Notation (1 of 2: Bounded intervals)
More resources available at www.misterwootube.com
From playlist Working with Functions
TabletClass Math http://www.tabletclass.com . This explains interval notation and set builder notation. Set notation is used in more advance math like Pre-Calculus and higher.
From playlist Pre-Calculus / Trigonometry
Using Clocks to Solve Fractions String 2
Another introductory video using clocks to understand fractions
From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents
Using Clocks to Solve Fractions String 6
Here we use the clock model to deal with 3/18 and 3/9
From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents
MATH3411 Information, Codes and Ciphers In this problem, we use arithmetic encoding and decoding. Presented by Thomas Britz, School of Mathematics and Statistics, Faculty of Science, UNSW Australia
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(IC 5.8) Near optimality of arithmetic coding
The expected encoded length of the entire message is within 2 bits of the ideal encoded length (the entropy), assuming infinite precision. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding
Application of Interval Arithmetic in Differential Equations Research
JirĂ Benedikt is a mathematician working in the theory of existence, uniqueness, and bifurcations of strongly nonlinear differential equations. At the Wolfram Technology Conference 2010, Benedikt discussed the application of interval arithmetic in differential equations research. For mo
From playlist Wolfram Technology Conference 2010
Eva Darulova : Programming with numerical uncertainties
Abstract : Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. Finite-precision arithmetic, such as fixed-point or floating-point, is a common and efficient choice, but introd
From playlist Mathematical Aspects of Computer Science
Computing Principal Eigenvalue in Interval Arithmetic
Jiri Benedikt
From playlist Wolfram Technology Conference 2019
Linear equations in smooth numbers - Lilian Matthiesen
Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for
From playlist Mathematics
The Green - Tao Theorem (Lecture 2) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Half-Isolated Zeros and Zero-Density Estimates - Kyle Pratt
50 Years of Number Theory and Random Matrix Theory Conference Topic: Half-Isolated Zeros and Zero-Density Estimates Speaker: Kyle Pratt Affiliation: University of Oxford Date: June 23, 2022 We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros
From playlist Mathematics
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
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