'Krylov subspace' presentation slideshows

Introduction to Model Order Reduction II.2 The Projection Framework Methods

Introduction to Model Order Reduction II.2 The Projection Framework Methods. Luca Daniel Massachusetts Institute of Technology with contributions from: Alessandra Nardi, Joel Phillips, Jacob White. Projection Framework: Non invertible Change of Coordinates. Note: q << N. reduced state.

1.12k views • 88 slides

The Life of SPICE as a Transient Circuit Simulator

The Life of SPICE as a Transient Circuit Simulator. Chung-Kuan Cheng CSE Department UC San Diego. Outline: SPICE (Simulation Program with Integrated Circuit Emphasis). Motivation and Contribution Theory and Algorithms Efforts to Improve the Simulator What I have learned

1.62k views • 66 slides

Exploiting Low-Rank Structure in Computing Matrix Powers with Applications to Preconditioning

Exploiting Low-Rank Structure in Computing Matrix Powers with Applications to Preconditioning. Erin C. Carson Nicholas Knight, James Demmel , Ming Gu U.C. Berkeley. Motivation: The Cost of an Algorithm. Algorithms have 2 costs: Arithmetic (flops) and m ovement of data (communication)

747 views • 63 slides

Krylov-Subspace Methods - I

Krylov-Subspace Methods - I. Lecture 6 Alessandra Nardi. Thanks to Prof. Jacob White, Deepak Ramaswamy, Michal Rewienski, and Karen Veroy. Last lecture review. Iterative Methods Overview Stationary Non Stationary QR factorization to solve Mx=b Modified Gram-Schmidt Algorithm QR Pivoting

596 views • 33 slides

Krylov-Subspace Methods - I

Krylov-Subspace Methods - I. Lecture 6 Alessandra Nardi. Thanks to Prof. Jacob White, Deepak Ramaswamy, Michal Rewienski, and Karen Veroy. Last lecture review. Iterative Methods Overview Stationary Non Stationary QR factorization to solve Mx=b Modified Gram-Schmidt Algorithm QR Pivoting

656 views • 33 slides

Krylov-Subspace Methods - II

Krylov-Subspace Methods - II. Lecture 7 Alessandra Nardi. Thanks to Prof. Jacob White, Deepak Ramaswamy, Michal Rewienski, and Karen Veroy. Last lectures review. Overview of Iterative Methods to solve Mx=b Stationary Non Stationary QR factorization Modified Gram-Schmidt Algorithm

619 views • 31 slides

The Landscape of Ax=b Solvers

382 views • 26 slides

Example:

Introduction to Krylov Subspace Methods. DEF:. Krylov sequence. Example:. Krylov sequence. 1 11 118 1239 12717 1 12 141 1651 19446 1 10 100 989 9546 1 10 106 1171 13332. 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 0 3 -1 8.

501 views • 24 slides

Example:

Introduction to Krylov Subspace Methods. DEF:. Krylov sequence. Example:. Krylov sequence. 1 11 118 1239 12717 1 12 141 1651 19446 1 10 100 989 9546 1 10 106 1171 13332. 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 0 3 -1 8.

246 views • 24 slides

CSE245: Computer-Aided Circuit Simulation and Verification

CSE245: Computer-Aided Circuit Simulation and Verification. Lecture Note 4 Model Order Reduction (2) Spring 2008 Prof. Chung-Kuan Cheng. Model Order Reduction: Overview. Explicit Moment Matching AWE, Pade Approximation Implicit Moment Matching (Projection Framework)

397 views • 21 slides

CSE245: Computer-Aided Circuit Simulation and Verification

CSE245: Computer-Aided Circuit Simulation and Verification. Lecture Note 4 Model Order Reduction (2) Spring 2010 Prof. Chung-Kuan Cheng. Model Order Reduction: Overview. Explicit Moment Matching AWE, Pade Approximation Implicit Moment Matching (Projection Framework)

214 views • 21 slides

CSE245: Computer-Aided Circuit Simulation and Verification

CSE245: Computer-Aided Circuit Simulation and Verification. Lecture Note 4 Model Order Reduction (2) Spring 2008 Prof. Chung-Kuan Cheng. Model Order Reduction: Overview. Explicit Moment Matching AWE, Pade Approximation Implicit Moment Matching (Projection Framework)

212 views • 21 slides

Simple iteration procedure

residue. use of pre-conditionner. correction. residue. use of pre-conditionner. Simple iteration procedure. Solve. Known approximate solution. Preconditionning:. Jacobi. Gauss-Seidel. Lower triangle. Spectral radius (magnitude of largest eigenvalue ). Convergence.

347 views • 13 slides

Example:

Introduction to Krylov Subspace Methods. DEF:. Krylov sequence. Example:. Krylov sequence. 1 11 118 1239 12717 1 12 141 1651 19446 1 10 100 989 9546 1 10 106 1171 13332. 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 0 3 -1 8.

313 views • 8 slides