Since a has a complete set of eigenvectors v", k=1,.n u, k-th eigenvector of RJ e=Re0=∑ck米(R)vk Fe=∑ck((R3) 3.2.1 Example SLIDE 27 We consider the situation in which the initial error only contains to modal components corresponding to k=1 and k figure below show the evolution of the error for each iteration. The faster of the k=5 mode can be readily observed0 2 4 6 8 10 12 14 16 18 20 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 n=20 λ(RJ) mode k v 2 (mode k=2) v 15 (mode k=15) 01.02468 ö❏÷✩ø▼ù✺úPû◗ü ý➥þ▼ÿ✁￾✄✂✆☎✞✝✠✟☛✡☞✟✌￾✎✍✑✏✆✒✁✓✔✂✖✕✗✂✘✡✖✂✙✕✚✍✜✛✘✂✛þ✣✢✤✂❲ÿ✦✥☛✂✄￾✖✕✗✍✑✧✄✡✚★✪✩✬✫✮✭✰✯✲✱✴✳✶✵✖✵✶✵✜✷✸✫ ✹✻✺✽✼✔✾✽✿❁❀❃❂ ✯ ❅❄ ✩❇❆❉❈❋❊✩ ★✪✩ ★✪✩✬✳✪✭✤● ✾✽❍■✿✖✼❑❏✴✿✶▲✬▼✴✿✶◆✙✾✽❖P✺◗❖✴❘✸❙❯❚ ❀ ❈❁✯ ❙❱❀❲❂ ✯❳❄❅ ✩✙❆✮❈❋❊✩❩❨✩❲❬❙❯❚❪❭ ★✪✩ ❀❃❫ ✯ ❙❋❫❴❀❲❂ ✯ ❅❄ ✩❇❆✮❈❋❊✩ ❬ ❨ ✩✠❬❙❯❚☛❭✽❭✜❫ ★✪✩ ❵✪❛❝❜❞❛❢❡ ❣❯❤❞✐❃❥❧❦✸♠❢♥ ö❏÷✩ø▼ù✺úPû✦♦ ♣✂❧￾✎✍❴ÿ❃✡✤þ❢q✴✂✖✧r✕s✝✠✂t✡✤þs✕✈✉✠✟✑✕❃þ❢✍❴ÿ✖þ▼ÿ①✇✮✝①þ❢￾✄✝②✕s✝✠✂Pþ▼ÿ♦þs✕❭þ❢✟❪✓✘✂✖✧❇✧✽✍❪✧❧✍❨ÿ✦✓④③⑤￾✎✍❴ÿ✠✕⑥✟❨þ▼ÿ✠✡⑦✕✗✍⑧✏⑨✍⑩q✴✟❪✓ ￾✄✍❪✏❶✒❃✍❴ÿ❷✂✛ÿ✠✕✈✡❸￾✄✍✑✧❇✧✽✂❇✡❹✒✠✍❨ÿ✁q❨þ▼ÿ✤✢✌✕⑥✍✘✭⑨✯✲✱✌✟❨ÿ✁q✘✭⑨✯❻❺✦❼ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 0.5 0 0.5 1 1.5 2 x sin(π x) sin(5 π x) e 0 n=20 0 2 4 6 8 10 12 14 16 18 20 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 λ(RJ) mode k 01.02468 ö❏÷✩ø▼ù✺úPû❃❽ ❾✝❃✂❩❿❉✢✑✉❲✧✎✂⑨➀✎✂✖✓✔✍✑✇❻✡✽✝❃✍✑✇➁✕➂✝❃✂➃✂✙✥❪✍❪✓④✉❲✕❭þ❢✍❨ÿ➄✍➅✛✘✕➂✝❃✂➃✂✙✧❇✧✽✍✑✧➆✛✙✍✑✧⑨✂✄✟P￾✎✝ þs✕⑥✂✙✧✎✟❪✕❭þ❢✍❨ÿ❷❼ ❾✝❃✂❩✛✙✟❪✡✄✕⑥✂✖✧ q✴✂✄￾✄✟❪③■✍✜✛❋✕➂✝❃✂➇✭✰✯➁❺➈✏⑨✍✶qP✂☞￾✄✟❴ÿ✻➀✄✂➉✧✎✂✎✟Pq❨þs✓④③■✍✴➀✙✡✙✂✖✧❇✥❪✂✎qP❼ ✱✴✱