Du befindest dich hier: FSI Informatik » Prüfungsfragen und Altklausuren » Hauptstudiumsprüfungen » Lehrstuhl 10 » anla-2016-03-02 (Übersicht)
no way to compare when less than two revisions
Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen der Seite angezeigt.
— | pruefungen:hauptstudium:ls10:anla-2016-03-02 [02.03.2016 14:09] (aktuell) – angelegt kili | ||
---|---|---|---|
Zeile 1: | Zeile 1: | ||
+ | **Examiner: | ||
+ | **Grade:** 1.0 | ||
+ | |||
+ | **Note:** | ||
+ | There were no exam protocols for this subject before my exam, so I created my own trainer for ANLA with 138 questions. It covers the lectures 1-15, as these are crucial for understanding the rest of the book. Take a look at it at [[http:// | ||
+ | |||
+ | **Atmosphere: | ||
+ | |||
+ | **Questions: | ||
+ | |||
+ | Gerschgorin’s Theorem (from exercises) | ||
+ | * He gave me a real symmetric matrix and asked me, what the Gerschgorin’s Theorem says about the location of the eigenvalues. | ||
+ | * What can I say about them regarding the symmetry of the matrix? | ||
+ | * Draw a diagram with the regions of the eigenvalues. | ||
+ | * Can eigenvalues lie on the edge of the disks? | ||
+ | * What can you say about eigenvalues of singular matrices? | ||
+ | |||
+ | Norms | ||
+ | * What three conditions must hold for a norm? | ||
+ | * How is a matrix norm defined and what is its meaning? | ||
+ | * What fourth condition holds for matrix norms? | ||
+ | |||
+ | Least Squares | ||
+ | * What is a Least Squares problem? | ||
+ | * What are the three ways to solve it? | ||
+ | * How do the three ways compare regarding their complexity? | ||
+ | * How do the three ways compare regarding their numerical stability? | ||
+ | |||
+ | Eigenvalue Algorithms | ||
+ | (the questions all referred to the lectures “Eigenvalue Problems” to “Reduction to Hessenberg Form” in the Book) | ||
+ | * What are the general steps to compute the eigenvalues of a matrix? | ||
+ | * Why can’t we directly compute the eigenvalues of a matrix that is not in Hessenberg form? | ||
+ | * Explain the simple version of the QR algorithm. | ||
+ | * How did we modify the QR Algorithm to get better results? | ||
+ | |||
+ | **Preparation for the exam:** | ||
+ | I read the book (“Numerical Linear Algebra” by Trefethen and Bau) from lecture 1 to 31 a couple of times. I tried to fully understand the chapters 1-15 and 24-27. I understood the basic concepts of the lectures 16-23 and 28-31. Although Prof. Rüde covered 1-38 in the lectures, this was the optimal preparation. |