Υπολογισμος τετραγωνικης ριζας

[Stormwatch]

Ξερει κανεις καποιο αλγοριθμο (μπακαλικο για να γινεται σε χαρτι και οχι επαναληπτικο για υπολογιστη) για τον υπολογισμο τετραγωνικης ριζας ακεραιου?Thanx.

[HdkiLLeR]

Koita sxetika me ton ipologismo tetragwnikwn rizwn iparxei mia epanalipsiti methodos twn Newton-Raphson opou simfona me ton opoio ean Y einai mia prosegisi tis tetragwnikis rizas enos arithmou x(oxi anagastika akeraiou alla opoioudipote pragmatikou) tote mia kaliteri prosegisi einai i (Y+x/Y)/2.Tora auto pou boreis na kaneis einai to exeis wse sto Y arxika tin timi 1(arxiki ipothesi oti i riza toy x einai to 1) kai meta adikathistas to Y diadoxika me ton parapanw ipologismo orizodas esy mia kali prosegisi tis rizas px otan oi dio diadoxikes prosegiseis diaferoun meta to 4o simadiko psifio.Diladi Y1:=1; Y2:=(Y1+x)/2; meta Y1:=Y2; Y2:=(Y1+x)/2; klp auto vasika borei na vrisketai mesa se mia epanalipsi i opoia tha teleiwnei otan Y2-Y1<=0,01 gia akriveia mexri 2 psifia meta tin ipodiastoli i Y2-Y1<=0.0001 analoga me tin akriveia poy thes.Telika enas proteinomenos algorithmos tha borouse na einai o exis:

----------

diavase x;

Y1:=1;

Y2:=(Y1+x)/2;

oso (Y2-Y1>0.001)

{

Y1:=Y2;

Y2:=(Y1+x)/2;

}

----------

Auta kai pisteuw na voithisa

[HdkiLLeR]

Koita sxetika me ton ipologismo tetragwnikwn rizwn iparxei mia epanalipsiti methodos twn Newton-Raphson opou simfona me ton opoio ean Y einai mia prosegisi tis tetragwnikis rizas enos arithmou x(oxi anagastika akeraiou alla opoioudipote pragmatikou) tote mia kaliteri prosegisi einai i (Y+x/Y)/2.Tora auto pou boreis na kaneis einai to exeis wse sto Y arxika tin timi 1(arxiki ipothesi oti i riza toy x einai to 1) kai meta adikathistas to Y diadoxika me ton parapanw ipologismo orizodas esy mia kali prosegisi tis rizas px otan oi dio diadoxikes prosegiseis diaferoun meta to 4o simadiko psifio.Diladi Y1:=1; Y2:=(Y1+x)/2; meta Y1:=Y2; Y2:=(Y1+x)/2; klp auto vasika borei na vrisketai mesa se mia epanalipsi i opoia tha teleiwnei otan Y2-Y1<=0,01 gia akriveia mexri 2 psifia meta tin ipodiastoli i Y2-Y1<=0.0001 analoga me tin akriveia poy thes.Telika enas proteinomenos algorithmos tha borouse na einai o exis:

----------

diavase x;

Y1:=1;

Y2:=(Y1+x)/2;

oso (Y2-Y1>0.001)

{

Y1:=Y2;

Y2:=(Y1+x)/2;

}

----------

Auta kai pisteuw na voithisa

[Dvs]

re hdkiller eipame oxi gia ipologisti! <p>

gia to xarti: <p>px. riza tou 9:<p>

9 |

3 |3

3 |3<p>are riza(9) = riza (3^2) = 3<p>

[auto legetai analisi se protous paragontes. osoi oroi einia ipsomenoi se artia dinami vginoun ektos apo tin riza me 1/2 ron ekteti kai loipa... poli mpakaliko alla doueleuei ]

[HdkiLLeR]

E kala more nomiza oti ithele algorithm

[bandito]

Enas algorithmos gia ipologismos rizas se xarti iparxei sto vivlio tis 2as i protis gimnasiou (den 3erw an iparxei akoma). Kanei gia ola akoma kai gia dekadikous kai einai sxetika eukolos. Moiazei me tin diairesi

[Stormwatch]

Thanx mages.Telika to vrika.Einai sto biblio tis 2as gimnasio opos eipe o bandito.

[Dvs]

pes ton kai mia re na ton doume kai emeis p