Isibalo samalensi ahlanganayo (ayi-convex)

Isihloko mayelana ne-Equation yamalensi ahlanganayo (convex)

Ngaphambi kokufunda i-equation yelensi eqondile, qonda imithetho yezimpawu zelensi eqondile ngezansi.

Imithetho yesibonakaliso selensi eqondile

– Ibanga lento (do)

Uma into idlula emsebeni wokukhanya, khona-ke ibanga lento lihle.

– Ibanga lesithombe (di)

Uma umsebe wokukhanya udlula isithombe, khona-ke ibanga lesithombe lihle (isithombe sangempela). Uma umsebe wokukhanya ungadluli esithombeni, ibanga lesithombe lihle (isithombe esibonakalayo).

– Ubude be-focal (f)

Uma umsebe wokukhanya udlula endaweni eqondile yelensi, ubude be-focal belensi buyi-positive. Ngokuphambene nalokho, uma umsebe wokukhanya ungadluli indawo eqondile yelensi, ubude be-focal belensi buyi-negative. Indawo eqondile yelensi eqondile idlula endaweni eqondile yokukhanya. Ngakho-ke, ubude be-focal belensi eqondile buyi-positive.

– Ukuphakama kwento (ho)

Uma into ingaphezu kwe-axis eyinhloko, khona-ke ukuphakama kwento kusayinwe kukuhle (into iqondile). Ngokuphambene nalokho, uma into ingaphansi kwe-axis eyinhloko yelensi eqondile, ukuphakama kwento kukubi (into iguquliwe).

– Ukuphakama kwesithombe (hi)

Uma isithombe singaphezu kwe-axis eyinhloko, ukuphakama kwesithombe kuqondile (isithombe siqondile). Uma isithombe singaphansi kwe-axis eyinhloko, ukuphakama kwesithombe kuphambene (isithombe siphendukezelwe).

– Ukukhulisa isithombe (m)

Uma ukukhulisa isithombe > 1, khona-ke usayizi wesithombe mkhulu kunosayizi wento. Uma ukukhulisa isithombe = 1, khona-ke usayizi wesithombe ulingana nosayizi wento. Uma ukukhulisa isithombe kungu-< 1, usayizi wesithombe mncane kunosayizi wento.

Isibalo selensi eqondile

Isibalo selensi ehlanganayo (eyi-convex) 1

s = do = ibanga lento, s' = di = ibanga lesithombe, ho = P P' = ukuphakama kwento, hi = Q Q' = ukuphakama kwesithombe, F 1 kanye no-F 2 = indawo egxile ilensi ehlanganayo.

Unxantathu we-P'AP ufana nonxantathu we-Q'AQ. Ngakho-ke:

Isibalo selensi ehlanganayo (eyi-convex) 2

Unxantathu BF 2 A = Q'F 2 Q lapho ibanga lika-AB = ukuphakama kwento (h) kanye nebanga lika-F2A = ubude obuqondile (f) belensi eqondile. Ngakho-ke:

Isibalo selensi ehlanganayo (eyi-convex) 3

Isibalo selensi ehlanganayo (eyi-convex) 4

do = ibanga lento (elihle uma into idlula ngokukhanya)

di = ibanga lesithombe (elihle uma isithombe sidlula ngokukhanya noma isithombe singokoqobo)

f = ubude bokugxila (obuhle uma indawo yokugxila yelensi eqondile idlula ngokukhanya)

Khumbula njalo imithetho yezimpawu zamalensi aqondile uma usebenzisa lesi sibalo ukuxazulula inkinga yamalensi aqondile.

Ukukhulisa isithombe (m)

Qaphela ukwakheka kwesithombe esingenhla. Njengonxantathu be-PAP 'ne-QAQ', singathola ubudlelwano phakathi kwebanga lento kanye nebanga lesithombe nokuphakama kwento kanye nokuphakama kwesithombe:

Isibalo selensi ehlanganayo (eyi-convex) 5

Isibalo esingenhla singabhalwa futhi njengoba singezansi ngokungeza uphawu u-m:

Isibalo selensi ehlanganayo (eyi-convex) 6

m = ukukhuliswa kwesithombe

ho = ukuphakama kwento (kuhle uma into ingaphezu kwe-axis eyinhloko yelensi eqondile noma into iqonde phezulu)

hi = ukuphakama kwesithombe (okungekuhle uma isithombe singaphansi kwe-axis eyinhloko yelensi eqondile noma isithombe siphendukezelwe)

do = ibanga lento (elihle uma into idlula ngokukhanya)

di = ibanga lesithombe (elihle uma isithombe sidluliswa ngokukhanya noma isithombe singokoqobo)