Ubuntu – How to find the best driver for the ATI graphics card


I'm trying to find the best graphics card for my ATI Radeon HD 7730M card (My machine has hybrid graphics, should I worry about installing a suitable driver for the intel vga too ?) because I'm having a bad experience with the open source version. It's like lots of crossing lines appear for a very fast glimpse and then disappear instantly without a trace. It's nothing big, but it's not usual nor acceptable. This happens randomly, every few minutes.

Here is as much information I could gather about my vga card by running the following commands:

$ sudo lshw (Only relevant information is listed here):

        description: VGA compatible controller
        product: Chelsea LP [Radeon HD 7730M]
        vendor: Advanced Micro Devices, Inc. [AMD/ATI]
        bus info: pci@0000:01:00.0
        version: 00
        clock: 33MHz
        capabilities: pm pciexpress msi vga_controller bus_master cap_list rom
        configuration: driver=radeon latency=0

$ Xorg -version

X.Org X Server 1.14.5
Release Date: 2013-12-12
X Protocol Version 11, Revision 0
Build Operating System: Linux 3.2.0-37-generic x86_64 Ubuntu
Current Operating System: Linux MG-7520SE 3.11.0-15-generic #23-Ubuntu SMP Mon Dec 9 18:17:04 UTC 2013 x86_64
Kernel command line: BOOT_IMAGE=/boot/vmlinuz-3.11.0-15-generic.efi.signed root=UUID=fdebe919-101f-4bc7-84c1-f209c05c18c8 ro quiet splash acpi_osi=Linux acpi_backlight=vendor quiet splash vt.handoff=7
Build Date: 17 December 2013  10:06:15AM
xorg-server 2:1.14.5-1ubuntu2~saucy1 (For technical support please see http://www.ubuntu.com/support) 
Current version of pixman: 0.30.2
    Before reporting problems, check http://wiki.x.org
    to make sure that you have the latest version.

$ lspci -nnk

01:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] Chelsea LP [Radeon HD 7730M] [1002:682f]
    Subsystem: Dell Device [1028:0572]
    Kernel driver in use: radeon

man radeon (I can't find my card listed anywhere !)

       The radeon driver supports PCI, AGP, and PCIe video cards based on the following ATI/AMD chips (note: list is non-exhaustive):

       R100        Radeon 7200
       RV100       Radeon 7000(VE), M6, RN50/ES1000
       RS100       Radeon IGP320(M)
       RV200       Radeon 7500, M7, FireGL 7800
       RS200       Radeon IGP330(M)/IGP340(M)
       RS250       Radeon Mobility 7000 IGP
       R200        Radeon 8500, 9100, FireGL 8800/8700
       RV250       Radeon 9000PRO/9000, M9
       RV280       Radeon 9200PRO/9200/9200SE/9250, M9+
       RS300       Radeon 9100 IGP
       RS350       Radeon 9200 IGP
       RS400/RS480 Radeon XPRESS 200(M)/1100 IGP
       R300        Radeon 9700PRO/9700/9500PRO/9500/9600TX, FireGL X1/Z1
       R350        Radeon 9800PRO/9800SE/9800, FireGL X2
       R360        Radeon 9800XT
       RV350       Radeon 9600PRO/9600SE/9600/9550, M10/M11, FireGL T2
       RV370       Radeon X300, M22
       RV410       Radeon X700, M26 PCIe
       R423/R430   Radeon X800, M28 PCIe
                   Radeon X1300/X1400/X1500/X1550/X2300
       RV530/RV560 Radeon X1600/X1650/X1700
                   Radeon X1200/X1250/X2100
       RV610/RV630 Radeon HD 2400/2600/2700/4200/4225/4250
       RV620/RV635 Radeon HD 3410/3430/3450/3470/3650/3670
       RS780/RS880 Radeon HD 3100/3200/3300/4100/4200/4250/4290

       CEDAR       Radeon HD 5430/5450/6330/6350/6370
       JUNIPER     Radeon HD 5750/5770/5830/5850/5870/6750/6770/6830/6850/6870
       HEMLOCK     Radeon HD 5970
       PALM        Radeon HD 6310/6250
       SUMO/SUMO2  Radeon HD 6370/6380/6410/6480/6520/6530/6550/6620
       BARTS       Radeon HD 6790/6850/6870/6950/6970/6990
       TURKS       Radeon HD 6570/6630/6650/6670/6730/6750/6770
       CAICOS      Radeon HD 6430/6450/6470/6490
       CAYMAN      Radeon HD 6950/6970/6990
       ARUBA       Radeon HD 7000 series
       TAHITI      Radeon HD 7900 series
       PITCAIRN    Radeon HD 7800 series
       VERDE       Radeon HD 7700 series
       OLAND       Radeon HD 8000 series
       HAINAN      Radeon HD 8000 series
       BONAIRE     Radeon HD 7790 series
       KAVERI      KAVERI APUs
       KABINI      KABINI APUs

Now as far as I could get, fglrx stable version of the driver supports only up to version 1.13 of xserver and I'm running 1.14, so I'm trying to use the open-source one instead. I opened the system's settings dialog, opened the "Software & Updates" dialog from there and switched to the "Additional Drivers" tab, where I confirmed that I'm using the open source version of ati drivers. I suppose their website is this one.

Now the latest version on the mentioned site is 7. How can I verify that I'm using the latest version ?

Based on this answer, I installed the ppa repository for the open source driver and ran sudo apt-get update && sudo apt-get upgrade, but nothing was downloaded. So I'm supposedly running the latest version, so how can I verify that ?