Introduction to Scientific Computing II Conjugate Gradients Dr Slides: 19 Download presentation Introduction to Scientific Computing II Conjugate Gradients Dr. Miriam Mehl Steepest Descent – Basic Idea • solution of SLE • minimization • iterative one-dimensional minima direction of steepest descent? Steepest Descent – Algorithm Steepest Descent – Algorithm II Steepest Descent – Example initial error after 1 iteration after 10 iterations Steepest Descent – Example h 1/16 1/32 1/64 1/128 iterations 646 2, 744 11, 576 48, 629 Steepest Descent – Convergence • Poisson with 5 -point-stencil like Jacobi Steepest Descent – Convergence Conjugate Gradients – Basic Idea • solution of SLE • minimization • iterative one-dimensional minima no repeating search directions Steepest Descent – Principle Conjugate Gradients – Principle CG – Algorithm Steepest Descent – Example initial error after 1 iteration after 10 iterations Conjugate Gradients – Example initial error after 1 iteration after 10 iterations Conjugate Gradients – Example h iterations sd iterations cg #unknowns 1/16 646 35 225 1/32 2, 744 76 961 1/64 11, 576 157 3, 969 1/128 48, 629 322 16, 129 CG – Convergence • Poisson with 5 -point-stencil like SOR no parameter adjustment PCG – Idea convergence rate cg: Solve system M-1 Ax=M-1 b better condition number k M-1 easy to apply PCG – Algorithm PCG – Algorithm Histogram of oriented gradients for human detectionPressure gradients in the heartHistograms of oriented gradients for human detectionSteep authority gradientConventional computing and intelligent computingPython ide for scientific computingBest gpu for scientific computingScientific computing tutorialScientific inquiry vs scientific methodHow is a scientific law different from a scientific theory?Regarder introduction to cloud computingIntroduction to parallel computing ananth gramaIntroduction to evolutionary computingIt 101 - introduction to computingCs101 vu edu pkIntroduction to mapreduce in cloud computingIntroduction to ubiquitous computingMobility of bits and bytesCs101 vu edu pkDistributed systems overview