Wiki143:WikiProject Mathematics/PlanetMath Exchange/41-XX Approximations and expansions

41A05 Interpolation

• PM: interpolation, id=5805 -- WP: interpolation -- Status: A

CryptoDerk 05:39, Feb 3, 2005 (UTC)

• PM: Lagrange Interpolation formula, id=229 -- WP: Lagrange polynomial -- Status: A

CryptoDerk 05:53, Feb 3, 2005 (UTC)

• PM: proof of uniqueness of Lagrange Interpolation formula, id=5577 -- WP: Lagrange polynomial -- Status: A

CryptoDerk 05:53, Feb 3, 2005 (UTC)

• PM: Simpson's 3/8 rule, id=4351 -- WP: Newton-Cotes formulas -- Status: A

Simpson's 3/8 is part of the NC formulas, and it is explained there. CryptoDerk 06:09, Feb 3, 2005 (UTC)

• PM: trapezoidal rule, id=4318 -- WP: trapezium rule -- Status: A

CryptoDerk 06:11, Feb 3, 2005 (UTC)

• PM: Vandermonde interpolation approach, id=5802 -- WP: polynomial interpolation -- Status: A

CryptoDerk 16:04, Feb 3, 2005 (UTC)

• PM: composite trapezoidal rule, id=8147^new! -- WP guess: composite trapezoidal rule -- Status:

• PM: lecture notes on polynomial interpolation, id=9116^new! -- WP guess: lecture notes on polynomial interpolation -- Status:

• PM: linear interpolation, id=9861^new! -- WP guess: linear interpolation -- Status:

41A10 Approximation by polynomials

• PM: proof of Weierstrass approximation theorem, id=6145 -- WP: Bernstein polynomial -- Status: A

CryptoDerk 07:10, Feb 3, 2005 (UTC)

• PM: Weierstrass approximation theorem, id=6143 -- WP: Stone-Weierstrass theorem -- Status: A

CryptoDerk 07:10, Feb 3, 2005 (UTC)

• PM: proof of Weierstrass approximation theorem in R^n, id=7603 -- WP guess: proof of Weierstrass approximation theorem in R^n -- Status:

41A25 Rate of convergence, degree of approximation

• PM: linear convergence, id=5824 -- WP: rate of convergence -- Status: A

CryptoDerk 07:12, Feb 3, 2005 (UTC)

• PM: quadratic convergence, id=5825 -- WP: rate of convergence -- Status: A

CryptoDerk 07:17, Feb 3, 2005 (UTC)

• PM: superconvergence, id=793 -- WP: superconvergence -- Status: C

CryptoDerk 17:27, Feb 3, 2005 (UTC)

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

• PM: Taylor series, id=709 -- WP: Taylor series -- Status: A

CryptoDerk 06:53, Feb 3, 2005 (UTC)

• PM: Taylor's Theorem, id=706 -- WP: Taylor's theorem -- Status: A

CryptoDerk 07:00, Feb 3, 2005 (UTC)

• PM: converse to Taylor's theorem, id=6823 -- WP guess: converse to Taylor's theorem -- Status:

• PM: example of Taylor polynomials for \sin x, id=6782 -- WP guess: example of Taylor polynomials for \sin x -- Status:

• PM: example of Taylor polynomials for the exponential function, id=6790 -- WP guess: example of Taylor polynomials for the exponential function -- Status:

• PM: example of use of Taylor's theorem, id=6826 -- WP guess: example of use of Taylor's theorem -- Status:

• PM: examples on how to find Taylor series from other known series, id=6825 -- WP guess: examples on how to find Taylor series from other known series -- Status:

• PM: getting Taylor series from differential equation, id=6831 -- WP guess: getting Taylor series from differential equation -- Status:

• PM: derivation of Taylor series, id=7268 -- WP guess: derivation of Taylor series -- Status:

• PM: approximate non-linear transformation of affine combination, id=9088^new! -- WP guess: approximate non-linear transformation of affine combination -- Status:

• PM: Taylor formula remainder: various expressions, id=7902^new! -- WP guess: Taylor formula remainder: various expressions -- Status:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

• PM: Approximation of the log function (small x), id=7113 -- WP: Mercator series -- Status: N

DavidCBryant 20:01, 12 January 2007 (UTC)

• PM: asymptotic bounds for factorial, id=7910^new! -- WP guess: asymptotic bounds for factorial -- Status:

41A99 Miscellaneous topics

• PM: approximation, id=5862 -- WP guess: approximation -- Status: