In fact, the eigenvalues are accumulating near one, an unsurprising result given that the eigenvalues of the discretized K operator were accumulating at zero 836o ercise 4 Estimate how many iterations will be needed for a 3 rylov- for the 1-d disc ample. Will the number of iterations increase as the discretization is refined? b or ercise 5 Suppose the integral equation were change 重(x)=0(x) r-aa(a')d For what value of a would the solution no longer be unique.(you can answer this Rast by looking at the eigenplot above).I Note 21 always have a unique solution. However, a first-kind equation almost never has a unique solution, the exception being when the green's function is singular, as we will investigate next lecture 3.9 SeconK KinK Theory 3.9.1Guh Lto I General Second kind integral equation )=a(x)/G(x,x)(x)dr’→重=(Ia (IKn)σ actions of What is重n?Kn? 39.2Di Ruprusuhtatioh n(a)=> onii (a) Pa=∑1(/0(x);(x)dx)()➦➧❃❦ß✳❈❥❱Ø❏✜Ü❥❏rt★✾á✾❲❁❄❧■✾❲❃◗♦✦❈❋▼❄❍★✾✜❣❯❈■❇P✾á❈■❱❲❱❲❍★❀➃❍❆▼❄❈❋❏P❁❄❃★❧➃❃★✾✜❈❋❇❯●■❃★✾❥Ü◗❈■❃✆❍★❃✤❣✐❍★❇r♣★❇r❁❄❣P❁❄❃★❧✉❇r✾✹❣P❍★▼é❏✪❧■❁❄♦■✾✹❃ ❏Pt✤❈✦❏✿❏Pt❆✾❼✾❲❁❄❧■✾❲❃◗♦✦❈❋▼❄❍★✾✜❣❯●■ß✔❏rt★✾✉❅✰❁⑤❣P❱❲❇P✾❲❏P❁✕❑❲✾✹❅ ☎ ●■♣✴✾❲❇❤❈✦❏r●■❇ÞÝ❯✾✹❇P✾❼❈❥❱❲❱✠❍❆❀➃❍★▼⑤❈✦❏r❁◆❃★❧q❈✦❏✲❑✹✾❲❇r●❆ã ✶ ✷✪✹×❈✺✼✻❉✽❀✿■× ✼ ❖➞❣✐❏P❁❄❀✇❈✦❏P✾✖t★●✦Ý ❀q❈■❃◗⑦æ❁◆❏P✾❲❇❤❈✦❏r❁◆●❥❃❆❣sÝ✿❁❄▼◆▼❹❊✤✾ ❃★✾❲✾✜❅✰✾✹❅ ß➯●❥❇Ú❈ ￾▲❇P⑦◗▼❄●✦♦✏à ❣P❍★❊❆❣P♣❆❈■❱❲✾✇❊❆❈■❣P✾✹❅➎❈❋▼❄❧■●❥❇P❁◆❏Pt❆❀ ❏P●è❱✠●■❃◗♦❥✾❲❇r❧■✾❹ß➯●■❇❼❏rt★✾ ë à③♥✄❅★❁❄❣r❱✠❇r✾✠❏r❁✧❑✹✾✹❅❬❣P✾✹❱✠●❥❃❆❅◗à③❖◗❁◆❃❆❅➥✾❲å✏à ❈❋❀q♣★▼❄✾■ã ■✶❁❄▼◆▼❭❏rt★✾q❃✏❍❆❀➃❊✴✾❲❇❼●❋ßÞ❁é❏r✾❲❇❤❈✦❏r❁◆●❥❃❆❣á❁◆❃❆❱❲❇P✾✜❈■❣P✾❂❈❥❣✬❏Pt★✾✇❅✰❁⑤❣P❱❲❇P✾❲❏P❁✕❑✹❈❋❏P❁❄●■❃Ú❁⑤❣▲❇r✾✛✚❆❃★✾✜❅❂ ✶✏✷✯✹×❈✺✼✻❉✽❊✿❋×➢➡ ●✰❍★♣★♣✴●❥❣P✾✬❏rt★✾❼❁❄❃❥❏r✾❲❧❥❇r❈■▼✮✾✹♠✏❍❆❈✦❏r❁◆●❥❃✆ÝÞ✾❲❇r✾❼❱❤t❆❈❋❃★❧❥✾✹❅✆❏P● ✂á➫➯➭✚➲➞➳✶➼➐➫✳➭✴➲ ✌ ✳ ￾ ✒ ➴ ✳ ➴ ✴ ➭➜✏➥➭➻ ✴ ➼➐➫➯➭➻ ➲✐➽✏➾➻ ✓ ❢★●❥❇✬Ý✿t✤❈✦❏▲♦②❈■▼◆❍❆✾❹●■ß ￾ Ý❯●❥❍★▼⑤❅❪❏Pt★✾✇❣P●■▼❄❍✰❏P❁❄●■❃Ú❃★●❘▼❄●■❃❆❧■✾❲❇á❊✴✾❹❍★❃❆❁❄♠✏❍★✾❥ã☎✖➯⑦■●❥❍è❱✹❈❋❃è❈■❃❆❣PÝ❯✾✹❇ ❏Pt❆❁❄❣✑￾⑥❍✤❣⑥❏❉❊◗⑦❦▼❄●◗●■❖◗❁◆❃❆❧q❈❋❏✪❏Pt★✾❼✾✹❁◆❧❥✾❲❃★♣★▼❄●❋❏❉❈■❊✤●✦♦❥✾❉✘Øã Ô➥Õ✮ÖØ×✏✎✔Ù Û❣❂❏rt★✾❚❈❋❊✴●✦♦■✾❪✾❲å◗✾✹❇r❱❲❁❄❣P✾☞❀q❈■❖■✾✜❣✇❱✠▼❄✾✹❈❋❇✜Ü❯❈➎❣P✾✹❱❲●■❃❆❅◗à③❖◗❁◆❃✤❅ ❁❄❃✏❏P✾❲❧❥❇r❈■▼✪✾✹♠✏❍❆❈✦❏r❁◆●❥❃ ❅★●✏✾✜❣q❃★●❋❏ ❈❋▼❄Ý✪❈②⑦◗❣➞t❆❈②♦■✾á❈➃❍❆❃★❁❄♠✏❍★✾❼❣P●■▼❄❍✰❏P❁❄●■❃✔ã❭❶❵●✦Ý❯✾✹♦■✾✹❇✹Ü◗❈ ✚✤❇r❣✐❏✐à③❖◗❁◆❃❆❅✆✾✹♠✏❍❆❈❋❏P❁❄●■❃✆❈■▼◆❀q●❥❣✐❏✪❃★✾❲♦❥✾❲❇✪t❆❈■❣ ❈❼❍★❃❆❁❄♠✏❍★✾á❣✐●❥▼◆❍✰❏r❁◆●❥❃✻Ü❥❏Pt★✾á✾✠å★❱✠✾✹♣✰❏P❁❄●■❃✇❊✴✾❲❁❄❃★❧❹Ý✿t★✾❲❃✇❏rt★✾❼❑á❇P✾✹✾❲❃❘❅ ❣➐ß➯❍★❃✤❱Ø❏P❁❄●■❃❘❁❄❣Þ❣P❁◆❃★❧❥❍★▼⑤❈❋❇✜Ü❥❈■❣ ÝÞ✾áÝ✿❁❄▼❄▼✻❁◆❃◗♦❥✾✹❣✐❏P❁❄❧❥❈✦❏r✾✬❃❆✾✠å◗❏❉▼◆✾✜❱Ø❏r❍★❇P✾❥ã ✢✪➊✂✁ ✄ ✩✞→✚↔➞➔✆☎✞✝➑✐➔✟☎✡✠➥➟✩✔↔ê➝☞☛ ☎✔➡✍✌✔➡ ❝ ✂✛◗✘✯✛❥✣✦✥★✧ ❅✔✣②✥❆❨❿✛✂✁➃✲❆✣②④ ✌ ✍✏✎✒✑✔✓➥➤★➤ ❑á✾❲❃❆✾❲❇❤❈❋▼❘●◗✾✹❱❲●■❃❆❅☞❖◗❁❄❃❆❅☞❁◆❃✏❏P✾✹❧■❇❤❈❋▼✚✾✹♠✏❍❆❈❋❏P❁❄●■❃ ➩❂➫➯➭✚➲➞➳æ➼➐➫➯➭✴➲ ✌ ✒ ➸✇➫➯➭✔➺P➭➻ ➲✐➼➐➫➯➭➻ ➲✐➽■➭➻ ❋ ➩ ➳ ➫ ✠ ✌ ☎è➲✐➼ ♥✬❁❄❣r❱✠❇r✾✠❏r✾á✾✜♠✏❍★❁◆♦✦❈■▼◆✾✹❃❥❏ ➩➚ ➳ ➫ ✠ ✌ ☎➚ ➲✰➼➚ Ý✿t★✾✹❇P✾➃➩á➚✆❈■❃❆❅❪➼❆➚☞❈❋❇r✾❵ß➯❍❆❃❆❱Ø❏r❁◆●❥❃❆❣✿●❋ß❭➭✔ã ■✶t❆❈❋❏❉❁❄❣❵➩á➚✏❂ ☎❦➚ ❂ ☎✔➡✍✌✔➡⑤➠ ❡☞✱✳✼✜❴❋✣✦✛✏✙✹✛❚✩á✫✮✭✯✱➯❛★✥★✧❜✛✏✘✚✙✇❫③✲✤✣ ✂✥★✧✳✛✏✣②④✻✱✳✘ ✌ ✍✏✎✒✑✔✓➥➤▲✝ ✝✛✏❩✯✣✦✛✏✼✜✛◗✘✚✙✹✥✰✙✜✱✳✲✴✘❬➼➚ ➫✳➭✴➲➞➳ ➪➚➹❄➘✞➴ ➼➚ ➹ ➷➹ ➫➯➭✚➲ ￾✣✦✲✏✎✜✛◗❴❋✙✜✱✳✲✴✘❿➼➚ ➳✒✑❼➼ ✑❼➼➢✍ ➪➚➹◆➘✯➴ ✓ ◗ ❽ ➱ ✃Ø➬ ➮ ✔✒ ➼➐➫✳➭✴➲ ➷➹ ➫✳➭✴➲✐➽■➭✖✕ ➷➹ ➫✳➭✴➲ ë ☛