Course plan

Material from the lectures (slides + ipad notes) can be found here.

Abbreviations and links can be found at the end of this page.

 

 

Week 44

Activity 0: Asynchronous learning

• Activity 0a: Block 1 application:  Data analytics
• Optional: Activity 0b: Quiz: Background and a bit (optional)

Activity 1: Lecture 1

• Reading: block1.pdf: §1.1 (except §1.1.7)
• Contents: Course Intro + RQ + PM, lecture demo: https://play.kth.se/media/SF2524%20Power%20method/0_z4msl6o5
• Recommended exercises: AL17: 1-10, AL19: 1-2, 1-3, AL20: 1-6a, AL21 1-1a-c  (abbreviations and links at the bottom of this page)

Activity 2: Asynchronous learning

• Activity 2a: Introduction to the active learning workspace environment
• Activity 2b: The minimization intepretation of the Rayleigh Quotient
• Link block 1 of the active learning workspace http://jarlebring.ddns.net/~jarl/active_learning/active_learning.php?id=8&contents=2 Links to an external site.
• Recommended exercise: ALW21: 1-19

Activity 3: Lecture 2

• Reading: block1.pdf: §1.1,§1.3
• Contents: Conv. theory PM + Inv. it + RQI + AM intro
• Recommended exercises:  ALW20: 1-17, 1-2, 1-26 (julia only), ALW19: 1-2

Activity 4: Asynchronous learning

• Reading: block1.pdf: §1.1.7
• Activity 4a: Rayleigh-Ritz method theory
• Recommended exercises: ALW22: 1-10, 1-12

Activity 5: Lecture 3

• Reading: block1.pdf: §1.2,§1.3
• Contents: CGS, MGS, RGS, AF +AM.
• Recommended exercises:  ALW20 1-10, 1-38, 1-21, 1-34, ALW21: 1-9,

Activity 6: Asynchronous learning

• Reading: block1.pdf: §1.3.3, §1.4.1
• Activity 6a: Lanczos method derivation
• Activity 6b: The epsilon_m quantity

 

Week 45

Activity 7: Lecture 4   (ZOOM ONLY)

• Reading: block1.pdf: §1.4
• Contents: Convergence AM + shift-and-invert
• Recommended exercises: AL20: 1-33, 1-46, AL19 1-31b, 1-39 

Activity 8: Asynchronous learning

• Activity 8a: Block 2 application: CPU-socket + iterative methods
• Activity 8b: Breakdown
• Recommended exercises: AL21: 2-22, AL20: 1-11

Activity 9: Lecture 5  - Replaced. See this message.

• Reading: block2.pdf: 2.1.1
• Contents: Linsys Intro + GMRES
• Recommended exercises: AL21: 2-8, AL18: 2-15

Activity 10: Asynchronous learning

• None - focus on homework

 

Week 46

Activity 11: Lecture 6

• Reading:  block2.pdf  §2.1.2
• Contents: GMRES conv. disks
• Recommended exercises: AL20:  2-4, 2-44, 2-29, 2-57, AL18: 2-20a, 2-24
  
• Recording: Zoom recording

Activity 12: Asynchronous learning

• Reading:  block2.pdf: §2.1.2, §2.5
• Activity 12a: GMRES convergence single outlier
• Activity 12b: Preconditioning for GMRES
• Recommended exercises: single outlier: AL22: 2-5,  GMRES preconditioning: AL21: 2-41,

Activity 13: Lecture 7

• Reading: block2.pdf §2.2
• Contents: CG + CG convergence
• Recommended exercises: AL20: 2-8, 2-50, AL21: 2-52, 2-99
  
• Recording: Zoom recording

Activity 14: Asynchronous learning

• Reading: block2.pdf. §2.2.3
• Activity 14a: Preconditioning CG part 1
• Activity 14b: Preconditioning CG part 2
• Recommended exercises: AL22 2-28, 2-30

Activity 15: Lecture 8

• Reading: block2.pdf  §2.3
• Contents: CGNE + GMRES preconditioning (cont)
• Recommended exercises: AL21: 2-23, 2-25, 2-37, AL20: 2-51, 2-53,
• Recording: Zoom recording links

Activity 16: Asynchronous learning

• Reading: block2.pdf  BiCG
• Activity 16a: BiCG method derivation
• Recommended exercises: AL22 2-32

Week 47

Activity 17: Lecture 9

• Reading:block3.pdf: §3.1-3.2
• Contents: Async recap +  Intro QR-algorithm
• Recommended exercises: AL21: 3-5, AL21: 3-3
• Recording: Zoom recording links

Activity 18: Asynchronous learning

• Reading: block3.pdf: §3.1
• Activity 18a: Intro to the QR-method by Driscoll

Activity 19: Lecture 10

• Reading: block3.pdf §3.2.1
• Contents:  QR-method. Improvement 1: phase 1
• Recommended exercises: AL21: 3-7, 3-9, 3-14, AL20: 3-12, 3-16, 3-32, 3-40
• Zoom recording: https://canvas.kth.se/courses/36060/discussion_topics/281465

Activity 20: Asynchronous learning

• Reading: block3.pdf:  §3.2
• Activity 20a: QR factorization by Householder reflectors (by van de Gijn)

Week 48

Activity 21: Lecture 11

• Reading: block3.pdf:  §3.2.2
• Contents: QR-method. Improvement 2: phase 2. Improvement 2 (start)
• Recommended exercises: AL21: 3-19, 3-8,
• Zoom recording: https://canvas.kth.se/courses/36060/discussion_topics/281465

Activity 22: Asynchronous learning

• Reading: block3.pdf: 
• Activity 22a: Simultaneous iteration part 1: Normalized and unnormalized
• Activity 22b: Simultaneous iteration part 2: Convergence of unnormalized (diagonal + triangular)
• Recommended exercises AL22: 3-6, 3-30

Activity 23: Lecture 12

• Reading: block3.pdf:  §3.3
• Contents:  Improvement 2 (cont) QR-method shifts, QR-method convergence theory
• Recommended exercises  AL21:  3-21 AL18: 3-2,

Activity 24: Asynchronous learning

• Reading: block3.pdf: 
• Activity 24a: QR method summary
• Activity 24b: Deflation in the QR-method

Week 49

Activity 25: Lecture 13

• Reading: block4.pdf: 4.1 
• Contents: Matrix functions intro + general methods
• Recommended exercises: AL18:  4-1, 4-3, 4-27, 4-33,  4-21, AL21: 4-5, 4-8, AL17: 4-9
• Zoom recording: https://canvas.kth.se/courses/36060/discussion_topics/283263

Activity 26: Asynchronous learning

•  Activity 26a: FOM derivation (preparation for Krylov approx of matrix functions)
• Recommended exercises: AL21 4-8.

Activity 27: Lecture 14

• Reading: block4.pdf: §4.2
• Contents:  Matrix exponention + Mat sqrt + Mat sign
• Recommended exercises: AL18: 4-18, 4-23, AL21: 4-22, 4-30
• Zoom recording: https://canvas.kth.se/courses/36060/discussion_topics/283263

Activity 28: Asynchronous learning

•   Activity 28a: phi-functions
• Recommended exercises: AL22: 4-16

Week 50

Activity 29: Lecture 15

• Reading: block4.pdf: §4.3
• Contents: Krylov approx for matrix functions. Exponential integrators applications
• Recommended exercises: AL21 4-24, AL17: 4-20

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Abbreviations:

block1.pdf: block1.pdf Download block1.pdf

block2.pdf: block2.pdf Download block2.pdf

block3.pdf: block3.pdf Download block3.pdf

block4.pdf: block4.pdf Download block4.pdf

t.b.a=to be announced (will be added later)

ALXX = Active learning workspace corresponding to year 20XX.

AL22 = http://jarlebring.ddns.net/~jarl/active_learning/active_learning.php?id=8&contents=3 Links to an external site.

AL21 = http://jarlebring.ddns.net/~jarl/active_learning/active_learning.php?id=1&contents=2 Links to an external site.

AL20 = Selected problems from Active learning workspace 2020 Download Selected problems from Active learning workspace 2020

AL19 = Selected problems from Active learning workspace 2019 Download Selected problems from Active learning workspace 2019

AL18 = Selected problems from Active learning workspace 2018 Download Selected problems from Active learning workspace 2018

AL17 = Selected problems from Active learning workspace 2017 Download Selected problems from Active learning workspace 2017

AL16 = Selected problems from Active learning workspace 2016 Download Selected problems from Active learning workspace 2016