PPT-CS 240A : 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 MatrixMatrix Multiplication DGEMM. 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. 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 . Dense A:. Gaussian elimination with partial pivoting (LU). Same flavor as matrix * matrix, but more complicated. Sparse A:. Gaussian elimination – Cholesky, LU, etc.. Graph algorithms. Sparse A:. Jianyu. Huang. , Leslie Rice,. Devin A. Matthews, Robert A. van de . Geijn. IPDPS2017, May 31. st. , Orlando, FL. Jianyu Huang. , Leslie Rice,. Devin A. Matthews, Robert A. van de . Geijn. The University of Texas at Austin. 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. ... ... …. A . matrix. . M. is an array of . cell entries. (. m. row,column. ) . that have . rectangular. . dimensions. (. Rows x Columns. ).. Example:. 3x4. 3. 4. 15. x. Dimensions:. A. a. row,column. A. 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. 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 . . 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. Tae Jun Ham. , Sung Jun Jung, . Seonghak. Kim, Young H. Oh, . Yeonhong. Park, . Yoonho. Song, Jung-Hun Park, . Sanghee. Lee, . Kyoung. Park, Jae W. Lee, . Deog-Kyoon. . Jeong. SEOUL NATIONAL.