PPT-Matrix Multiplication

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. m. ultiply. t. imes. l. ots. . of. X. 3 x 2 = 6. 5 x 2 = 10. Here are some arrays to show what multiply means.. 3 lots of 2 are 6. 5 lots of 2 are 10. When we multiply, we are. r. eally adding together lots of. Communication Avoiding. Fast. Algorithm for. Sparse Matrix . Multiplication. Part I: Minimizing arithmetic operations. Oded Schwartz. CS294, Lecture #21 Fall, 2011. Communication-Avoiding Algorithms. Written Methods. Written Methods. Throughout their years at school, children should progress from informal jottings and number line methods to formal efficient written methods.. By the end of Year 3, children should be confident using short efficient written methods for all four operations + - x ÷. Multiplication and Division 9. 5 x 10 = 50. Multiplication and Division 9. 50 . x 10 = . 500. 500 . x 10 = . 5000. Multiplication and Division 9. 205 . x 10 = . 2050. 250 . x 10 = . 2500. 25 . x 10 = . Tamás Herendi, S. Roland Major. UDT2012. Introduction. The presented work is . based on the algorithm by . T. Herendi . for constructing uniformly distributed linear recurring sequences to be used for pseudo-random number . 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. 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. Using Matrices Matrix A represents the number of points scored in each quarter for the first 4 games of football played by Frederick High School. Matrix B represents the number of points scored in each quarter for the first 4 games of football played by Thomas Johnson High School. Write a matrix that represents the combined points scored per quarter for the first four games. X X Groups of Multiply Multiplication Multiplied by Double Near double Array Repeated addition Expanded grid Compact grid Long multiplication Partition Place value Vertical multiplication Row Column Approaches of BCG Matrix. Components of BCG Matrix. Applications of BCG Matrix. Advantages of BCG Matrix . Limitations of BCG Matrix . ?. The BCG Matrix . . .. High. Low. Relative position (Market Share). 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.. Principle and Permutations. 4. Use the multiplication counting principle to determine the number of ways to complete a process involving several steps.. Use . factorials to count the number of permutations of a group of individuals. .