introduction Sergiy Pereverzyev PhD student at Fraunhofer Institut - PowerPoint PPT Presentation

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: Fraunhofer Institut Prof. H.Neunzert Techno- und Prof. R.Pinnau WirtschaftsMathematik, Dr. N.Siedow Department Transport Processes, Kaiserslautern, Germany . – p.1/3

introduction Sergiy Pereverzyev PhD student at Sci.supervisors: Fraunhofer Institut Prof. H.Neunzert Techno- und Prof. R.Pinnau WirtschaftsMathematik, Dr. N.Siedow Department Transport Processes, Sci.interests: regularization Kaiserslautern, Germany of inverse problems . – p.1/3

regularized fixed-point u : ˆ Fu = y . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G Au = y − Gu . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G Au k +1 = y − Gu k . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G Au k +1 = y δ − Gu k . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G A ∗ Au k +1 = A ∗ ( y − Gu k ) . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G u k +1 = ( A ∗ A ) † A ∗ ( y − Gu k ) . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G u k +1 = ( A ∗ A ) † A ∗ ( y − Gu k ) u α k +1 = g α ( A ∗ A ) A ∗ ( y δ − Gu k ) . – p.2/3

regularized fixed-point u : ˆ Fu = y F = A + G u k +1 = ( A ∗ A ) † A ∗ ( y − Gu k ) u α k +1 = g α ( A ∗ A ) A ∗ ( y δ − Gu k ) δ u − u α � ˆ k +1 � ≤ ϕ ( α ) + λ ( α ) + ρ � ˆ u − u k � . – p.2/3

balancing principle δ u − u α � ≤ ϕ ( α ) + � ˆ λ ( α ) ∆ = { α i , i = 1 , . . . , N } . – p.3/3

balancing principle δ u − u α � ≤ ϕ ( α ) + � ˆ λ ( α ) ∆ = { α i , i = 1 , . . . , N } � � � � u α i − u α j � ≤ � 4 δ i opt = max λ ( α j ) , j = 1 , . . . , ( i − 1) i . – p.3/3

balancing principle δ u − u α � ≤ ϕ ( α ) + � ˆ λ ( α ) ∆ = { α i , i = 1 , . . . , N } � � � � u α i − u α j � ≤ � 4 δ i opt = max λ ( α j ) , j = 1 , . . . , ( i − 1) i u − u α i opt � ≤ b ( δ ) � ˆ . – p.3/3

balancing principle δ u − u α � ≤ ϕ ( α ) + � ˆ λ ( α ) ∆ = { α i , i = 1 , . . . , N } � � � � u α i − u α j � ≤ κ � 4 δ i opt = max λ ( α j ) , j = 1 , . . . , ( i − 1) i u − u α i opt � ≤ b ( δ ) � ˆ . – p.3/3

balancing principle δ u − u α � ≤ ϕ ( α ) + � ˆ λ ( α ) ∆ = { α i , i = 1 , . . . , N } � � � � u α i − u α j � ≤ κ � 4 δ i opt = max λ ( α j ) , j = 1 , . . . , ( i − 1) i u − u α i opt � ≤ b ( δ ) � ˆ Hui Cao RICAM, Group Inverse Problems . – p.3/3