PPT-High Performance Linear System Solvers with Focus on Graph Laplacians

Richard Peng Georgia Tech Based on recent works joint with Serban Stan Yale Haoran Xu MIT Shen Chen Xu CMU Saurabh Sawlani GaTech John Gilbert UCSB. Lecturer: . Qinsi. Wang. May 2, 2012. Z3. high-performance theorem . prover. being developed at Microsoft Research.. mainly by Leonardo de . Moura. and . Nikolaj. . Bjørner. . . Free (online interface, APIs, …) . Based on. http://www.cs.engr.uky.edu/~. lewis/cs-heuristic/text/integer/linprog.html. The . bipartite graph matching problem.  is to find a set of unconnected edges which cover as many of the vertices as possible. If we select the set of edges. Recall…. Linear Equation. = equation in the form:. . ax. + . by. = c. Highest Power (Degree) = 1. Non-Linear Equation. = an equation in a form other than linear . Degree > 1. . To tell if an equation is linear:. Identifying functions . on tables, graphs, and equations.. Irma Crespo 2010. Warm Up. Graph y = 2x + 1. Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.. What is the linear equation for this graph?. Teaching & Learning Conference. Jane Nolan MBE. Entrepreneur in Residence and Development Officer (Careers Service). Katie Wray. Lecturer in Enterprise (SAgE Faculty). Entrepreneurial Students. Some statistics:. Pajdla. The Art of Solving Minimal Problems . Tricks: . Making Minimal Solvers Fast. Microsoft Research Cambridge. Czech Technical University in Prague. Capturing Reality . s.r.o. .. CapturingReality. Nishant Totla. , . Aditya. . Devarakonda. , . Sanjit. . Seshia. SAT Solving. Given a propositional logic formula in conjunctive normal form (CNF), does there exist a satisfying assignment?. . Define appropriate quantities from a situation, choose and interpret the scale and the origin for the graph, and graph the piecewise linear function.. Learning Goal . 2 . (HS.N-Q.A.1, 2, 3):. The student will be able to use units to solve multi-step contextual problems. Preprocessing. Can . Efficiently. . Simulate. Resolution. Paul . Beame. *. . Ashish Sabharwal. . *. Computer Science and Engineering, University of Washington, Seattle, WA, USA. . Allen Institute for Artificial Intelligence, Seattle, WA, USA. Define appropriate quantities from a situation, choose and interpret the scale and the origin for the graph, and graph the piecewise linear function.. Learning Goal . 2 . (HS.N-Q.A.1, 2, 3):. The student will be able to use units to solve multi-step contextual problems. Quiz. Tell true or false of the following statement:. . . . If c < 0, a < b, then ac > . bc. .. Linear Equation. A linear equation in one variable is an equation that can be written in the form:. Richard Peng. Georgia Tech. OUtline. (Structured) Linear Systems. Iterative and Direct Methods. (. Graph) . Sparsification. Sparsified. Squaring. Speeding up Gaussian Elimination. Graph Laplacians. 1. VS Experiments 2008 . –. Toronto, Canada. Leonardo de Moura. Microsoft Research. Agenda. What is SMT?. Experiments:. Windows kernel verification.. Extending SMT solvers.. Garbage collector (Singularity) verification. Sriram Rajamani. (based on notes/slides by Matt Fredrickson, Andre . Platzer. , . Emina Torlak and Leonardo . De Moura). Modern SAT solvers. First convert a formula to CNF (Conjunctive Normal Form). Use variant of DPLL (Davis Putnam .