First Steps in CUDA

CUDA programming has its sources in http://www.nvidia.com/object/cuda_get.html

First attempt was unsuccessful with NVidia Drivers. So I check the CUDA site for new sources. Just my luck I have found a beta driver for notebooks. We have GeForce 8400M GS. It works after installing the last beta driver.

When we run DeviceQuery with Visual Studio C++ Express Edition, the get the following output.

cuda-device-query

cuda-device-query

Gauss – Seidel Method

Gauss – Seidel Method is a method to solve linear equations with a numeric approach. It is one step ahead of Jacobi method. If Gauss-Seidel method converges, then Jacobi converges either. The reverse is not true. But if Gauss-Seidel converges, it converges faster than Jacobi.

The following code is an implementation in MATLAB.

gauss-seidel-method

Windows 7 Beta Experience (10 Points)

Windows 7

Windows 7

We have been using Vista at least one year on my wife’s notebook.  Even notebook has the top features, Yeliz has been frustrated about lots of problems with Vista. So we downloaded and installed Windows 7 Beta to our notebook. We have been using it for about 3 months. The satisfaction is very ahead of the Vista even we are using a Beta version. It seems to us that Vista’s destiny would be like ME.  I am going to list 13 points about our experience.

2) Overall fast performance exploring, coping and starting applications

2) Workgroup password enabled

3) Family control feature for Parental Control

5) Automatic desktop background changer

5) Snipping tool a customized print screen

6) Windows Defender is gone

7) Internet Explorer download bar when minimized

8) Advanced cascading window style with closing button for each instance

9) Drivers: All drivers are automatically installed except audio driver for Dell Inspiron 1420. This audio driver was more problematic with Vista.

10) Applications

Firefox 3.0 : O.K.

OpenOffice 3.0 : O.K.

GOM Player : O.K.

VLC Player : O.K.

MatLAB 7 : Failure with an error associated with java.swing when starting the application, however there is no problem of installing it.

Fractals with Newton Raphson Method

How to generate fractals with MatLAB?

A complex polynomial is used to find generate a fractal image. Newton Raphson method is used to accomplish the aim.

Also any complex polynomial can be used, ours is:

f (z) = z6 + (2 – 4i)z5 – z + (2 – 4i)

This has 6 roots.  We are going iterate over a matrix, which will give us the initial guess to feed the Newton Raphson method. And the root which is found with that intial guess is associated with a color. That color is marked in that matrix. The color will be graded with the iteration count in the Newton Raphson which represents the speed of convergence.

This is the MatLAB source code:

fractal code

This is the image produced:

Fractal with Newton Raphson

Fractal with Newton Raphson

Newton Raphson Yöntemi

Doğrusal olmayan denklemleri çözmek için kullanılan yöntemlerden biri de Newton-Raphson Yöntemi.  Bu yöntem ile eğer denklem bir köke yakınsıyorsa, hız bir şekilde kökün bulunması sağlanabiliyor. Tabii diğer sayısal yöntemler gibi kapsamadığı durumlar mevcut. Ekteki MatLAB kodu bu yöntemin bir gerçekleştirimini içermekte. Kullanıcı gireceği bir denklem için, belirleyeceği ilk tahmin değerine göre Newton-Raphson yöntemini uygulayabilir.

newtonraphson-matlab-code

1. Döngü

2. Döngü

3. Döngü

Referanslar: http://numericalmethods.eng.usf.edu/mtl/gen/03nle/index.html

http://www.mathworks.com/matlabcentral/fileexchange/4313

Yukarıdaki çizgeler f = x / (x^2+1) denklemi için, -0.3500 noktası başlangıç tahmini olarak gerçekleşmiş olan Newton Raphson yönteminin çalışma sürecini göstermektedir.
Aynı denklemi, -0.7000 noktası başlangıç tahmini yapılarak gerçekleştirildiği zaman ise yöntem köklere yakınsamamaktadır. Bu yöntemin açıklarından biri olan yansıma noktası (inflection point) durumuna örnek olmuştur. Anlamlı bir çizgeler oluşmadığı için ilgili görüntüler buraya eklenmemiştir.