'Partial pivoting' presentation slideshows

Gaussian Elimination

1.33k views • 88 slides

Parallel Programming in C with MPI and OpenMP

Parallel Programming in C with MPI and OpenMP. Michael J. Quinn. Chapter 12. Solving Linear Systems. Outline. Terminology Back substitution Gaussian elimination Jacobi method Conjugate gradient method. Terminology. System of linear equations Solve Ax = b for x Special matrices

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Sparse Matrix Methods on High Performance Computers

Sparse Matrix Methods on High Performance Computers. X. Sherry Li xsli@lbl.gov http://crd.lbl.gov/~xiaoye CS267/EngC233: Applications of Parallel Computers March 16, 2010. Sparse linear solvers . . . for unstructured matrices. Solving a system of linear equations Ax = b Iterative methods

738 views • 50 slides

CM0368 Scientific Computing

CM0368 Scientific Computing. Spring 2009 Professor David Walker david@cs.cf.ac.uk. Schedule. Weeks 1 & 2 ( 6 ): Numerical linear algebra (DWW) Solving A x = b by Gaussian elimination and Gauss-Seidel. Algebraic eigenvalue problem. Power method and QR method.

477 views • 47 slides

Chapter 14 Gaussian Elimination (IV) Bunch-Kaufman diagonal pivoting (partial pivoting)

Chapter 14 Gaussian Elimination (IV) Bunch-Kaufman diagonal pivoting (partial pivoting). Speaker: Lung-Sheng Chien.

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Part 3 - Chapter 9 Linear Systems of Equations: Gauss Elimination

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Linear Systems

637 views • 41 slides

Linear Systems

564 views • 41 slides

Sparse Direct Solvers on High Performance Computers

Sparse Direct Solvers on High Performance Computers. X. Sherry Li xsli@lbl.gov http://crd.lbl.gov/~xiaoye CS267: Applications of Parallel Computers March 2, 2005. Review of Gaussian Elimination (GE). Solving a system of linear equations Ax = b First step of GE: Repeats GE on C

548 views • 40 slides

Simultaneous Linear Equations

Simultaneous Linear Equations. Topic: Gaussian Elimination. Gaussian Elimination. One of the most popular techniques for solving simultaneous linear equations of the form Consists of 2 steps 1. Forward Elimination of Unknowns. 2. Back Substitution. Forward Elimination.

1.6k views • 38 slides

Scientific Computing

739 views • 36 slides

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 10. LU Decomposition and Matrix Inversion. Introduction. Gauss elimination solves [A] {x} ={B}

832 views • 32 slides

Lecture 11-II

Lecture 11-II. Iterative approaches for solving linear systems Successive over-relaxation Post-nonlinear system Partial pivoting. Derivation of Successive over-relaxation. Successive over-relaxation method. D=diag(diag(A)); U=triu(A)-D; L=A-triu(A); R=D+w*L; T= inv(R)* ((1-w)*D-w*U);

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Computational Physics (Lecture 6)

Computational Physics (Lecture 6) . PHY4370. Matrix Operations. Matrix operations involved in many numerical and analytical scientific problems. Schemes developed for the matrix problems can be applied to the related problems encountered in ordinary and partial differential equations.

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Design of parallel algorithms

Design of parallel algorithms. Linear equations Jari Porras. Linear equations. a 0,0 x 0 + ... + a 0,n-1 x n-1 = b 0 ... a n-1,0 x 0 + ... + a n-1,n-1 x n-1 = b n-1 Ax = b Usually solved in 2 stages reduce into upper triangular system Ux = y back-substitution x n-1 ... x 0

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CS 240A: Solving Ax = b in parallel

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Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)

Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs) Nejhum Shahed Office Hours: 2-5pm Wed, E309. Elementary Elimination Matrices. Example: Gaussian Elimination. Example: Gaussian Elimination. Example: Gaussian Elimination. LU Factorization.

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Linear Triangular System

249 views • 24 slides

Linear Systems Pivoting in Gaussian Elim.

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Introduction to Numerical Analysis I

Introduction to Numerical Analysis I. PA=LU. MATH/CMPSC 455. Partial Pivoting. Why? (1) zeros pivot; (2) swapping rows reduces possibility of rounding errors and poor scaling contaminating the solution. How?

251 views • 5 slides