11 - MATHEMATICS 54 Professor Constantin Teleman 9/29/09...

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MATHEMATICS 54 Professor Constantin Teleman 9/29/09 Lecture 10 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. ANNOUNCEMENTS *There will be a 30-minute quiz next Monday. It will be counted as double-credit and will cover the material before the midterm. Ask your TA tomorrow about this since they might adjust it. *And again there will be a regular quiz next Wednesday. *If you have any particular questions about the midterm grading, ask your TA first. LECTURE Eigenvalues, eigenvectors and Digitalization A will be a square ( n x n ) matrix. Question: compute A N for large values of N. Question: compute p(A) for a polynomial p. Compute exp(A) for some other analytic function. Problem with brute force attack: expensive n 3 ops for computing a product of n x n matrices, might be interested in large N asymptotics—not easy to guess. A = 3.3 4.8 1.6 2.3 B = 3.7 5.4 1.8 2.6 C = 4.1 6 2 2.9 N →∞ , A N 00 , B N 46 2 3 , C N 2 3 Application of computing A N Fibonaccis’s rabbits Year 0, 1 adult pair Year 1, 1 adult pair + 1 juvenile pair Year 2, 2 adult pair+ 1juvenile pair Question: How many rabbits after N years?
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This note was uploaded on 12/01/2009 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.

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11 - MATHEMATICS 54 Professor Constantin Teleman 9/29/09...

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