Polynomial interpolation yog ib txoj hauv kev kwv yees qhov tseem ceeb ntawm cov ntaub ntawv paub cov ntsiab lus. … Tus nqi ntawm tus exponent loj tshaj plaws yog hu ua degree ntawm polynomial. Yog hais tias ib pawg ntawm cov ntaub ntawv muaj n cov ntsiab lus paub, ces muaj ib tug polynomial ntawm degree n-1 los yog me dua uas hla tag nrho cov ntsiab lus.
Koj txhais li cas los ntawm polynomial interpolation?
Hauv kev txheeb xyuas tus lej, polynomial interpolation yog interpolation ntawm cov ntaub ntawv muab los ntawm polynomial ntawm qib qis tshaj plaws uas dhau los ntawm cov ntsiab lus ntawm dataset.
Yuav ua li cas koj pom qhov cuam tshuam ntawm polynomial?
Siv lub rooj. Thaum cov kev sib faib sib txawv tau suav, peb tuaj yeem suav qhov sib cuam tshuam polynomial f(x) muaj degree ≤n siv cov qauv hauv qab no. Newton tus faib qhov txawv formula f(x)=f[x0]+(x−x0)f[x1, x0]+(x−x0)(x−x1)f[x2, x1, x0]+(x−x0)(x−x1)(x−x2)f[x3, x2,x1, x0]+⋯+(x−x0)⋯(x−xn−1)f[xn, …, x0].
Puas yog interpolation polynomial tshwj xeeb?
Theorem 4.1 Uniqueness of interpolating polynomial. Muab cov ntsiab lus x0 < x1 < ··· < xn, muaj tsuas yog ib qho polynomial uas cuam tshuam cov haujlwm ntawm cov ntsiab lus ntawd. Pov thawj Cia P(x) thiab Q(x) yog ob qho kev sib cuam tshuam polynomials ntawm degree ntawm feem ntau n, rau tib pawg ntawm cov ntsiab lus x0 < x1 < ··· < xn.
Yuav ua li cas yog qhov yuam kev hauv polynomial interpolation?
n. ces lub sij hawm yuam kev raupolynomial interpolation siv cov nodes xi yog. E(x)=|f(x) −P(x)| ≤ 1 . 2n(n + 1)!
