Hessian matrix optimization yog dab tsi?
Hessian matrix optimization yog dab tsi?

Video: Hessian matrix optimization yog dab tsi?

Video: Hessian matrix optimization yog dab tsi?
Video: HESSIAN METHOD :Optimisation of Multivariable function #HESSIANMatrix #optimisation #NET #GATE 2024, Kaum ib hlis
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Siv hauv kev ua kom zoo

Hessian matrices yog siv nyob rau hauv loj-scale kev ua kom zoo teeb meem nyob rau hauv Newton-hom txoj kev vim hais tias lawv yog cov coefficient ntawm lub quadratic lub sij hawm ntawm ib lub zos Taylor Expansion ntawm ib tug muaj nuj nqi

Yog li ntawd, dab tsi yog Jacobian matrix siv rau?

?ˈko?bi?n/, /d??-, j?-/) ntawm vector-valued function inseveral variables yog qhov matrix ntawm tag nrho nws cov thawj-orderpartial derivatives.

Tsis tas li ntawd, Hessian matrix qhia peb li cas? Hauv lej, the Hessian matrix los yog Hessian yog square matrix ntawm thib ob-order partialderivatives ntawm scalar-valued muaj nuj nqi, los yog scalar teb. Nws piav qhia txog qhov curvature hauv zos ntawm kev ua haujlwm ntawm ntau yam hloov pauv.

Tsis tas li ntawd, dab tsi yog gradient vector?

Cov gradient yog ib lo lus zoo rau derivative, orthe rate of change of a function. Nws yog ib vector (ib txoj kev txav mus los) ntawd. Cov ntsiab lus nyob rau hauv cov kev taw qhia ntawm qhov loj tshaj qhov nce ntawm afunction (intuition ntawm vim li cas)

Puas yog Jacobian ib txwm zoo?

Cov cheeb tsam yog ib txwm zoo , yog li thaj tsam ntawm ib qho me me parallelogram hauv xy-space yog ib txwm tus nqi kiag ntawmthe Jacobian lub sij hawm lub cheeb tsam ntawm qhov sib thooj rectanglein uv-chaw. Hloov chaw, cia peb coj x = −5u, sog'(u) = −5 yog qhov tsis zoo. Now e−x/5=eu anddx=−5du.

Pom zoo: