Chebyshev-Gauss to'rtligi - Chebyshev–Gauss quadrature

Yilda raqamli tahlil Chebyshev-Gauss to'rtligi ning kengaytmasi Gauss kvadrati quyidagi turdagi integrallarning qiymatini yaqinlashtirish usuli:

{displaystyle int _ {- 1} ^ {+ 1} {frac {f (x)} {sqrt {1-x ^ {2}}}}, dx}

va

{displaystyle int _ {- 1} ^ {+ 1} {sqrt {1-x ^ {2}}} g (x), dx.}

Birinchi holda

{displaystyle int _ {- 1} ^ {+ 1} {frac {f (x)} {sqrt {1-x ^ {2}}}}, dxapprox sum _ {i = 1} ^ {n} w_ {i } f (x_ {i})}

qayerda

{displaystyle x_ {i} = cos chap ({frac {2i-1} {2n}} pi ight)}

va vazn

{displaystyle w_ {i} = {frac {pi} {n}}.}

^[1]

Ikkinchi holda

{displaystyle int _ {- 1} ^ {+ 1} {sqrt {1-x ^ {2}}} g (x), dxapprox sum _ {i = 1} ^ {n} w_ {i} g (x_ {) i))}

qayerda

{displaystyle x_ {i} = cos chap ({frac {i} {n + 1}} pi ight)}

va vazn

{displaystyle w_ {i} = {frac {pi} {n + 1}} sin ^ {2} chap ({frac {i} {n + 1}} pi ight).,}

^[2]

Shuningdek qarang

^ Abramovits, M va Stegun, men A, Matematik funktsiyalar bo'yicha qo'llanma, Tuzatishlar bilan 10-nashr (1972), Dover, ISBN 978-0-486-61272-0. Tenglama 25.4.38.
^ Abramovits, M va Stegun, men A, Matematik funktsiyalar bo'yicha qo'llanma, Tuzatishlar bilan 10-nashr (1972), Dover, ISBN 978-0-486-61272-0. Tenglama 25.4.40.