Gauss Elimination

๊ฐ€์šฐ์Šค ์†Œ๊ฑฐ๋ฒ•์€, ์—ฐ๋ฆฝ๋ฐฉ์ •์‹์˜ ํ•ด๋ฅผ ํ–‰๋ ฌ์„ ์ด์šฉํ•ด ์‰ฝ๊ฒŒ ๊ตฌํ•˜๋Š” ๋ฐฉ๋ฒ•์ด๋‹ค.

๊ธฐ๋ณธ์ ์œผ๋กœ ํ–‰๋ฒกํ„ฐ์˜ ๊ณ„์ˆ˜๋ฅผ ์กฐ์ž‘ํ•˜์—ฌ ๊ตฌํ•˜๋Š” ๋ฐฉ๋ฒ•์œผ๋กœ,

Upper Triangle Matrix, Lower Triangle Matrix ๋ฅผ ๋งŒ๋“ค์–ด ๊ตฌํ•˜๋Š” ๋ฐฉ๋ฒ•์ด๋‹ค.

์—ญํ–‰๋ ฌ์„ ๊ตฌํ•˜์—ฌ ๋‹ต์„ ์ฐพ๋Š” ๋ฐฉ์‹์€ Cost๊ฐ€ ๋งŽ์ด ๋“ค์–ด, ํ•ด๋ฅผ ๊ตฌํ•˜๋Š”๋ฐ๋Š” ์ ํ•ฉํ•˜์ง€ ์•Š๋‹ค.

์ž์„ธํ•œ ๋ฐฉ๋ฒ•์€ ์ƒ๋žตํ•œ๋‹ค.

Gauss-Jordan Method

๊ฐ€์šฐ์Šค- ์กฐ๋ฅด๋‹น ๋ฐฉ๋ฒ•์˜ ๊ฐ€์žฅ ํฐ ์ด์ ์€, ์—ญํ–‰๋ ฌ ์„ ๊ตฌํ•˜๋Š”๋ฐ์— ์žˆ๋‹ค.

๊ธฐ์กด์˜ Cramerโ€™s rule์„ ์‚ฌ์šฉํ•˜๋Š” ๊ฒƒ์€ computing cost๊ฐ€ ๋งŽ์ด ๋“ค๊ธฐ ๋•Œ๋ฌธ์—, ์ด ๋ฐฉ๋ฒ•์ด ๋งค์šฐ ์œ ์šฉํ•˜๋‹ค.

์—ญํ–‰๋ ฌ์„ ๊ตฌํ•˜๋Š”๋ฐ ์žˆ์–ด Gauss Elimination์—์„œ ํ•œ ํ–‰๋ฒกํ„ฐ๋ฅผ ์กฐ์ž‘ํ•ด์„œ ํ•˜๋Š” ๋ฐฉ๋ฒ•์€ ๋™์ผํ•˜๋‹ค.