Chebyshev nodes, the Glossary

Table of Contents

1. 16 relations: Affine transformation, Algebraic number, Approximation theory, Chebyshev polynomials, Diameter, Interval (mathematics), Maximum and minimum, Monic polynomial, Numerical analysis, Polynomial interpolation, Projection (linear algebra), Real number, Runge's phenomenon, Society for Industrial and Applied Mathematics, Unit circle, Zero of a function.

2. Algebraic numbers

Affine transformation

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.

See Chebyshev nodes and Affine transformation

Algebraic number

An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients. Chebyshev nodes and algebraic number are algebraic numbers.

See Chebyshev nodes and Algebraic number

Approximation theory

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Chebyshev nodes and approximation theory are numerical analysis.

See Chebyshev nodes and Approximation theory

Chebyshev polynomials

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x).

See Chebyshev nodes and Chebyshev polynomials

Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle.

See Chebyshev nodes and Diameter

Interval (mathematics)

In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".

See Chebyshev nodes and Interval (mathematics)

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function.

See Chebyshev nodes and Maximum and minimum

Monic polynomial

In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

See Chebyshev nodes and Monic polynomial

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

See Chebyshev nodes and Numerical analysis

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset.

See Chebyshev nodes and Polynomial interpolation

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.

See Chebyshev nodes and Projection (linear algebra)

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

See Chebyshev nodes and Real number

Runge's phenomenon

In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.

See Chebyshev nodes and Runge's phenomenon

Society for Industrial and Applied Mathematics

Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community.

See Chebyshev nodes and Society for Industrial and Applied Mathematics

Unit circle

In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.

See Chebyshev nodes and Unit circle

Zero of a function

In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).

See Chebyshev nodes and Zero of a function

See also

Algebraic numbers

• Algebraic integer
• Algebraic number
• Chebyshev nodes
• Constructible number
• Eisenstein integer
• Fundamental theorem of ideal theory in number fields
• Gaussian integer
• Geometric Constructions
• Hard hexagon model
• Imaginary unit
• Look-and-say sequence
• Perron number
• Pisot–Vijayaraghavan number
• Principal root of unity
• Quadratic irrational numbers
• Rational numbers
• Root of unity
• Roth's theorem
• Salem number
• Twelfth root of two

References

[1] https://en.wikipedia.org/wiki/Chebyshev_nodes

Also known as Chebyshev extrema, Chebyshev node, Chebyshev spacing, Chebyshev zeros, Gauss-Chebyshev points.