weekly update

- What is the OpenGL Context look like? A structure in C? An object is attached to a target (a pointer in C), then the state machine use the target to get and set the value of the object? http://www.arcsynthesis.org/gltut/Basics/Intro%20What%20is%20OpenGL.html

- profiling. Mac上的shark比较流行，可惜在windows上没有.

Download Windows SDK, v7.1, to get the xperf application and play with it.

xperf http://msdn.microsoft.com/en-us/performance/cc825801.aspx and Process Explorer.

Debugging Tools for Windows (x64)

Microsoft Windows Performance Toolkit

Microsoft Windows SDK v7.1

a similar profiler from AMD http://developer.amd.com/tools/CodeAnalyst/Pages/default.aspx

- 继续看[Introduction to Linear Algebra]里面的subspace, column space, null space的概念。

Column space contains all the right hand sides, in which case the Ax = b is solvable. The Null space N(A) contains all the solutions of Ax = 0.

- 继续读[Scientific Computing: An Introductory Survey by Michael Heath]

1. 在书中解nonlinear equations system or optimization的例子时候终于知道跟linear system ( system of linear equations )的关系了, 用iterative methods解前者的问题时候每一步都迭代中很可能需要解一个线性方程组来得到下一步走向的信息. 例如在P158 5.2.3, Newton's Method for One dimension nonlinear equation: use a linear line to fit the curve at every step.

2. 怎么求解minimization of quadratic function/energy (which is quadratic object function without constraints)?, for example min||Bx - b||^2 -> f(x) = x^t*B^t*B*x - B^t*b*x -> A = B^t * B, a = B^t * b,

Ax=b, which A is spd, can be solved by conjugate gradient method.