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Jan 08, 2024 238 likes •418 views

introduction Sergiy Pereverzyev PhD student at Fraunhofer Institut Techno- und WirtschaftsMathematik, Department Transport Processes, Kaiserslautern, Germany . p.1/3 introduction Sergiy Pereverzyev PhD student at Sci.supervisors:

SLIDE 1

introduction

Sergiy Pereverzyev

PhD student at Fraunhofer Institut Techno- und WirtschaftsMathematik, Department Transport Processes, Kaiserslautern, Germany

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SLIDE 2

introduction

Sergiy Pereverzyev

PhD student at Fraunhofer Institut Techno- und WirtschaftsMathematik, Department Transport Processes, Kaiserslautern, Germany Sci.supervisors:

Prof. H.Neunzert
Prof. R.Pinnau
Dr. N.Siedow

. – p.1/3

SLIDE 3

introduction

Sergiy Pereverzyev

PhD student at Fraunhofer Institut Techno- und WirtschaftsMathematik, Department Transport Processes, Kaiserslautern, Germany Sci.supervisors:

Prof. H.Neunzert
Prof. R.Pinnau
Dr. N.Siedow

Sci.interests: regularization

f inverse problems

. – p.1/3

SLIDE 4

regularized fixed-point

ˆ u: Fu = y

. – p.2/3

SLIDE 5

regularized fixed-point

ˆ u: Fu = y F = A + G

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SLIDE 6

regularized fixed-point

ˆ u: Fu = y F = A + G Au = y − Gu

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SLIDE 7

regularized fixed-point

ˆ u: Fu = y F = A + G Auk+1 = y − Guk

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SLIDE 8

regularized fixed-point

ˆ u: Fu = y F = A + G Auk+1 = yδ − Guk

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SLIDE 9

regularized fixed-point

ˆ u: Fu = y F = A + G A∗Auk+1 = A∗(y − Guk)

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SLIDE 10

regularized fixed-point

ˆ u: Fu = y F = A + G uk+1 = (A∗A)†A∗(y − Guk)

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SLIDE 11

regularized fixed-point

ˆ u: Fu = y F = A + G uk+1 = (A∗A)†A∗(y − Guk) uα

k+1 = gα(A∗A)A∗(yδ − Guk)

. – p.2/3

SLIDE 12

regularized fixed-point

ˆ u: Fu = y F = A + G uk+1 = (A∗A)†A∗(y − Guk) uα

k+1 = gα(A∗A)A∗(yδ − Guk)

ˆ u − uα

k+1 ≤ ϕ(α) + δ λ(α) + ρˆ

u − uk

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SLIDE 13

balancing principle

ˆ u − uα ≤ ϕ(α) +

δ λ(α)

∆ = {αi, i = 1, . . . , N}

. – p.3/3

SLIDE 14

balancing principle

ˆ u − uα ≤ ϕ(α) +

δ λ(α)

∆ = {αi, i = 1, . . . , N} iopt = max

i
uαi − uαj ≤

4δ λ(αj), j = 1, . . . , (i − 1)

. – p.3/3

SLIDE 15

balancing principle

ˆ u − uα ≤ ϕ(α) +

δ λ(α)

∆ = {αi, i = 1, . . . , N} iopt = max

i
uαi − uαj ≤

4δ λ(αj), j = 1, . . . , (i − 1)

u − uαiopt ≤ b(δ)

. – p.3/3

SLIDE 16

balancing principle

ˆ u − uα ≤ ϕ(α) +

δ λ(α)

∆ = {αi, i = 1, . . . , N} iopt = max

i
uαi − uαj ≤ κ

4δ λ(αj), j = 1, . . . , (i − 1)

u − uαiopt ≤ b(δ)

. – p.3/3

SLIDE 17

balancing principle

ˆ u − uα ≤ ϕ(α) +

δ λ(α)

∆ = {αi, i = 1, . . . , N} iopt = max

i
uαi − uαj ≤ κ

4δ λ(αj), j = 1, . . . , (i − 1)

u − uαiopt ≤ b(δ)

Hui Cao

RICAM, Group Inverse Problems

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