PPT-Matrix Multiplication and

Graph Algorithms Uri Zwick Tel Aviv University November 2016 1 Algebraic matrix multiplication Strassen s algorithm Rectangular matrix multiplication Boolean matrix multiplication Simple reduction to integer matrix multiplication. Communication Avoiding. Fast. Algorithm for. Sparse Matrix . Multiplication. Part I: Minimizing arithmetic operations. Oded Schwartz. CS294, Lecture #21 Fall, 2011. Communication-Avoiding Algorithms. Final presentation. One semester – winter 2014/15. By : Dana Abergel and Alex . Fonariov. Supervisor : . Mony. . Orbach. High Speed Digital System Laboratory. Abstract . Matrix multiplication is a complex mathematical operation.. Start from r.h.s , if there is any carry in any part ,it is to be added to next part.. A B . C D. C*A (D.A + B*C) B*D. 1 2. 4 3. 1*4 1*3+4*2 2*3. 4 11 6. 4+1 1 6. 5 1 6. and . Graph Algorithms. Uri Zwick. Tel Aviv University. February . 2015. Last updated: June 10, 2015. Algebraic matrix multiplication. Strassen. ’s algorithm. Rectangular matrix multiplication. Boolean matrix multiplication. Matrix multiplication I : parallel issues. Matrix multiplication II: cache issues. Thanks to Jim Demmel and Kathy Yelick (UCB) for some of these slides. Matrix-Matrix . Multiplication (“DGEMM”). Matrix Multiplication. Matrix multiplication is defined differently than matrix addition. The matrices need not be of the same dimension. Multiplication of the elements will involve both multiplication and addition. m. movies. v11. …. …. …. vij. …. vnm. V[. i,j. ] = user i’s rating of movie j. n . users. Recovering latent factors in a matrix. m. movies. n . users. m. movies. x1. y1. x2. y2. ... ... …. Janie Everett. EDT 605. Week One Assignment. Brain Rules Lesson Plan . *All citations are listed in slide notes*. What are Brain Rules?. There are12 brain rules. Rules about how the brain works. Can be used to enhance business and educational settings. 2. Module 3 Overview. 3. Read the Module Overview independently.. Mark important information that will help the implementation of this module.. Module 3 Overview. 4. Re-read the Overview to find your table’s assigned Topic. So what’s new about fractions in Grades 6-8?. SOL 6.4 . The student will . demonstrate multiple representations . of multiplication and division of fractions. . 2. Thinking About Multiplication. 3. Graph Algorithms. Uri Zwick. Tel Aviv University. Algebraic matrix multiplication. Strassen. ’s algorithm. Rectangular matrix multiplication. Boolean matrix multiplication. Simple reduction to integer matrix multiplication. . . 36. X 23. THINK:. 36 X 3. . FIRST. . 36. X 3. 3 X 6 = 1. 8. Carry the one. 3 X 3 = 9 and one more is . 10. Prior Knowledge Check. Evaluate:. 10 x 7 =. 3 x 9 = . 5 x 8 = . 6 x 2 = . 7 x 4 = . Work out. 1) 3 x 90 =. 2) 6 x 70. 3) 2 x 80. 4) 60 x 4. 5) 80 x 5 . What does:. The 8 in 82 represent?. The 4 in 47 represent?. Independent Events. 4. Use the multiplication rule for independent events to calculate probabilities.. Calculate . P. (at least one) using the complement rule and the multiplication . rule for . independent events..