数値計算の呪いとあそぼぅ！！/ the curse of numerical calculus

VRC LT #8

Transcript

1. ਺஋ܭࢉͷढ͍ͱ͋ͦ΅͎ʂʂ ΀ʹ (ehlfin_puni / punilfin) 2020/05/15
2. ͜͡͠ΐ͏͔͍ ͳ·͑ɿ΀ʹ VRC ID : ehlfin_puni Twitter : punilfin 2020/02/10 ʹ VRC ʹ͖·ͨ͠ 2 ϲ݄͔͚ͯ΍ͬͱ User ʹͳΓ·ͨ͠ ͖͢ɿ͢͏͕͘ ʮ͚ΜΖΜ͓͑ͯ͠ʯ͍ͬͯΘΕ·͢ɽͲ͏͢Ε͹͍͍Ͱ͔͢ ͖͢͡Όͳ͍ɿ΀Ζ͙ΒΈΜ͙ ΏΔͤͳ͍ɿුಈখ਺఺਺ (floating point number)
3. ࠓ೔఻͍͑ͨ͜ͱ ਓؒͷ௚ײ͸৴༻Ͱ͖ͳ͍ ܭࢉػʹ͸༗ݶͷढ͍͕͔͔͍ͬͯΔ ·ͱΊɿ͡Μ͍ͤ͸ͭΒ͖͘ͼ͍͠
4. ࠷ॳͷ؍࡯ ํఔࣜ x + y = 3 x + 1:0001y = 3:0002 Λղ͘ͱɼx = 1; y = 2ɽ ਓؒͷ௚ײ ʮํఔࣜΛগ͠ม͑ͨ͘Β͍ͳΒ౴͑΋গ͔͠͠มΘΒͳ͍ʯ ஫ҙ Ұൠ࿦ͱͯ͠ɼਓؒͷ௚ײ͸·ͬͨ͘৴༻Ͱ͖ͳ͍ ͦͷΑ͏ͳྫ͸ຕڍʹ͍ͱ·͕ͳ͍
5. ࠷ॳͷ؍࡯ ํఔࣜ x + y = 3 x + 1:0001y = 3:0001 Λղ͘ͱɼx = 2; y = 1ɽ ݁࿦ ํఔࣜʹ 0:0001 ͷมߋΛՃ͑Δͱ౴͕͑ 1ʢ0:0001 ͷ 1 ສഒʣมΘͬͨ ஫ҙ Ұൠ࿦ͱͯ͠ɼਓؒͷ௚ײ͸·ͬͨ͘৴༻Ͱ͖ͳ͍ ͜ͷྫΛݟͯ΋ɼਓؒͷ௚ײ͸·ͬͨ͘৴༻Ͱ͖ͳ͍͜ͱ͕Θ͔Δ
6. ܭࢉػ ݱ࣮ͷਓؒ͸ܭࢉػͳ͠Ͱ͸฻Βͤͳ͍ ढΘΕͨ࢓༷ɿܭࢉػ͸༗ݶͷ෦඼Ͱߏ੒͞Ε͍ͯΔͷͰɼಛʹϝϞϦ͕༗ݶ ܭࢉػʹ͓͚Δ਺ͷදݱʀුಈখ਺఺਺ a.k.a. ༗ݶͷढ͍ ʢ୯ਫ਼౓ͷ৔߹ʣ͍͍ͩͨ༗ޮ਺ࣈ 7 ܻ͔ 8 ܻ·Ͱද͢͜ͱ͕Ͱ͖Δ ͦΕҎ্͸ϝϞϦʹࡌΔΑ͏ʹແཧ΍ΓؙΊͯ͠·͏ʢؙΊޡࠩʣ ͖͞΄Ͳͷ௚ײΛഁյ͢Δݱ৅ͱ૊Έ߹ΘͤΔͱͭΒ͍͜ͱʹͳΔ
7. ՐΛਧ͘ढ͍ ුಈখ਺఺਺ͷ࢓༷ʹΑΓɼԋࢉͷͨͼʹ༗ޮ਺ࣈ 7 ܻͷͱ͜Ζʹ͸ޡ͕ࠩຖճೖΔ ੈͷதʹ͸ɼ໰୊ͷζϨ෯Λ 1 ສʢ4 ܻʣഒͯ͠౴͑ʹ൓ө͢Δํఔ͕͍ࣜΔ ͋ΘͤΔͱ༗ޮ਺ࣈ 3 ܻ͘Β͍͔͠৴༻Ͱ͖ͳ͘ͳΔ ΏΔͤͳ͍ Ͳ͏͢Δ͔ 1 ໰୊͔Β໨Λഎ͚ͯಀ͛ग़͢ ໰୊͕ղ͚ΔΑΓ΋ੜ͖͍ͯ͘΄͏͕େࣄͱ͍͏͜ͱ΋͋Δ 2 ͭΒ͍ࢥ͍Λ͠ͳ͕Βढ͍ͱٔΕΔ ͍·ݱࡏͰ΋ʮ࿈ཱҰ࣍ํఔࣜʹ͓͚Δ਺஋ղ๏ͷܾఆ൛ʢ͜Ε͚ͩ࢖͑͹೚ҙͷਓ͕ؒ͋͠ ΘͤʹͳΕΔํ๏ʣ ʯ͸ݟ͔͍ͭͬͯͳ͍ ߦྻͷ৚݅਺ͳͲΛ࢖ͬͯޡࠩղੳ͢Δ͜ͱ͸Մೳ ղ͖͍ͨ໰୊ͷಛੑΛΑ͘ݟͯ͋Ε͜Εͱ޻෉ΛڽΒ͢͜ͱʹͳΔ ͏·͘޻෉͕ϋϚΔͱ͍͍ײ͡ʹղ͚ΔͷͰͨͷ͍͠Β͍͠ ʢ͜ͷ͋ͨΓͷ࿩ɼڵຯ͸͋Δ͚Ͳ࢓ࣄͰ΋झຯͰ΋͍·ͷͱ͜Ζ΍Εͦ͏ʹͳ͍ʜʣ
8. ·ͱΊ ͡Μ͍ͤ͸ͭΒ͖͘ͼ͍͚͠Ͳͨ·ʹͨͷ͍͠