Scilab/C4/Linear-equations-Iterative-Methods/Khasi

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Time Narration
00:01 Paralok, ngi pdiangsngewbha ia phi sha ka Spoken Tutorial halor ka Solving System of Linear Equations using Iterative Methods.
00:10 Ha kaba kut jong kane ka jinghikai, phin sa nang ban:
00:14 Solve ia ka system jong ki linear equations da kaba pyndonkam ia ki iterative methods
00:18 Develop Scilab code ban solve ia ki linear equations.
00:22 Ban record ia kane ka jinghikai , nga pyndonkam da ka
00:25 Ubuntu 12.04 kum ka operating system
00:28 Bad ka Scilab 5.3.3 version.
00:33 Shwa ban pyrshang ia kane ka jinghikai, u nongpule udei ban don ia ki jingtip ba donkam jong ka
00:38 Scilab, bad solving linear equations.
00:42 Na ka bynta ka Scilab, sngewbha peit ia ki jinghikai ba iadei ba don ha ka Spoken Tutorial website.
00:50 Ka iterative method ba nyngkong kaba ngin pule kadei ka Jacobi method.
00:56 La ai ka system of linear equations, with n equations and n unknowns,
01:02 Ngi thoh ia ki equations ha kata ka rukom ba x of i k plus one is equal to b i minus summation of a i j x j k from j equal to one to n divided by a i i ha kaba i udei naduh one to n.
01:24 Ngi shu shim ia ki values na ka bynta man u x of i.
01:27 Nangta ngi bujli ia ki values ha ki equations ba la ioh na ka kyrdan ba hashwa.
01:34 Ngi bteng ia ka iteration haduh ba ka solution kan converge.
01:39 To ngin solve ia kane ka nuksa da kaba pyndonkam ia ka Jacobi Method.
01:44 To ngin peit ia u code na ka bynta ka Jacobi Method.
01:48 Ngi pyndonkam ia ka format method ban pynthikna ia ka format jong ki jubab ba la pyni ha ka Scilab console.
01:56 Hangne e u kdew ba ka jubab kadei ban dei ha ka scientific notation.
02:01 Bad twenty ka batai ia ki number jong ki digits ba dei ban pyni.
02:06 Nangta ngi pyndonkam ia ka input function ban ioh ia ki values na ka bynta
02:10 the matrices coefficient matrix,
02:12 right hand side matrix,
02:14 initial values matrix,
02:17 maximum number of iteration and
02:19 convergence tolerance.
02:22 Nangta ngi pyndonkam ia ka size function ban peit lada ka A matrix kadei ka square matrix.
02:29 Lada kam dei, ngi pyndonkam ia ka error function ban pyni ia ka jingbakla.
02:34 Nangta ngi peit lada ka matrix Akadei ka diagonally dominant.
02:40 Ka bynta ba nyngkong ka khein ia ka sum jong man kawei ka row jong ka matrix.
02:45 Nangta ka peit lada arsien ka product jong u diagonal element ka heh ban ia ka sum jong ki elements jong kata ka row.
02:54 Lada kam dei, ka jingbakla la pyni da kaba pyndonkam ia ka error function.
03:01 Lada ngi define ia ka function Jacobi Iteration ryngkat bad ki input arguments
03:07 A, b , x zero,
03:09 maximum iteration bad tolerance level.
03:14 Hangne x zero udei u initial values matrix.
03:19 Ngi peit lada ka size jong ka A matrix bad initial values matrix ki iabiang kawei bad kawei pat.
03:28 Ngi khein ia u value na ka bynta x k p one bad nangta peit lada ka relative error ka kham rit ban ia ka tolerance level.
03:38 Lada ka kham rit ban ia ka tolerance level, ngi break ia ka iteration bad ka solution la pynphai.
03:45 Khatduh eh ngi end ia ka function.
03:48 To ngin save bad execute ia ka function.
03:51 Phai sha ka Scilab console.
03:54 To ngin pyndap ia ki values ha man kawei pa kawei ka prompt.
03:57 U coefficient matrix A is open square bracket two space one semi colon five space seven close square bracket
04:08 Nion Enter.
04:10 Nangta ngi type: open square bracket eleven semicolon thirteen close square bracket
04:17 Nion Enter.
04:20 Ki initial values matrix is open square bracket one semi colon one close square bracket
04:28 Nion Enter.
04:30 Ka maximum number of iterations kadei arphewsan.
04:34 Nion Enter.
04:36 Ai ba ka convergence tolerance level be zero point zero zero zero zero one
04:44 Nion Enter.
04:46 Ngi call ia ka function da kaba type
04:48 Jacobi Iteration open parenthesis A comma b comma x zero comma M a x I t e r comma t o l close parenthesis
05:04 Nion Enter.
05:06 Ki values na ka bynta x one bad x two la pyni ha ka console.
05:11 Ki number jong ki iterations la pyni hangne.
05:14 To ngin pule mynta ia ka Gauss Seidel method.
05:19 La ai ia ka system of linear equations ryngkat bad n equations bad n unknowns
05:26 Ngi thoh biang ia ki equations na ka bynta man kawei pa kawei ka unknown
05:29 Da kaba subtract ia kiwei pat ki variables ryngkat bad ki coefficients jong ki na u element ba iadei na ka liang ka mon
05:37 Nangta ngi divide ia kane da u coefficient a i i of the unknown variable' for that variable.
05:45 Kane la leh na ka bynta man kawei pa laweo ka equation ba la ai.
05:49 Ha ka Jacobi method, na ka bynta ka computation jong u x of i k plus one, man ki element jong x of i k la pyndonkam lait nohx of i k plus one .
06:03 Ha ka Gauss Seidel method, ngi thoh nalor jong u value x of i k da x of i k plus one.
06:12 To ngin solve ia kane ka nuksa da kaba pyndonkam ia ka Gauss Seidel Method.
06:17 To ngin iapeit ia u code na ka bynta ka Gauss Seidel Method.
06:21 Ka lain banyngkong ka batai ia ka format jong ka jubab ba la pyni ha ka consoleda kaba pyndonkam ia ka format function.
06:29 Nangta ngi pyndonkam ia ka input function ban ioh ia ki values jong
06:32 coefficient matrix,
06:34 right hand side matrix,
06:36 initial values of the variables matrix,
06:38 maximum number of iterations bad
06:40 tolerance level.
06:43 Nangta ngi define ia ka function Gauss Seidel ryngkat bad ki input arguments A comma b comma x zero comma max iterations bad ka tolerance level bad ka output argument solution.
06:58 Ngi peit lada ka matrix A is square bad ki size jong initial vector and matrix A ki iabiang lang da kaba pyndonkam ia ka size bad ka length function.
07:10 Nangta ngi sdang ia ki iterations.
07:13 Ngi equate ia ki initial values vector x zero to x k.
07:19 Ngi shna ia ka matrix of zeros bad kajuh ka size jong x k bad khot ia ka x k p one.
07:28 Ngi solve na ka bynta man kawei pa kawei ka equation ban ioh ia u value jong u unknown variable na ka bynta katei ka equation da kaba pyndonkam ia u x k p one.
07:38 Ha man kawei pa kawei ka iteration, u value jong x k p one u kylla.
07:44 Kumjuh ruh, ngi peit lada ka relative error ka kham rit ban ia ka tolerance level ba la kdew.
07:50 Lada ka dei ,ngi break ia ka iteration.
07:54 Nangta ngi equate ia u x k p one sha u variable solution.
07:59 Khatduh eh ngi end ia ka function.
08:02 To ngin save bad execute ia ka function.
08:06 Phai sha ka Scilab console.
08:09 Na ka bynta ka prompt banyngkong , ngi type matrix A.
08:12 Type open square bracket two space one semi colon five space seven close square bracket
08:21 Nion Enter. Na ka bynta ka prompt babud,
08:24 type open square bracket eleven semi colon thirteen close square bracket
08:31 Nion Enter.
08:33 Ngi ai ia ki values jong initial value vector da kaba type
08:38 open square bracket one semicolon one close square bracket .
08:43 Nion Enter.
08:45 Nangta ngi batai ia u maximum number of iterations ba un dei arphewsan.
08:50 Nion Enter.
08:52 To ngin define ia ka 'tolerance level ban dei zero point zero zero zero zero one.
08:58 Nion Enter.
09:01 Khatduh eh ngi call ia ka function da kaba type
09:04 G a u s s S e i d e l open parenthesis A comma b comma x zero comma M a x I t e r comma t o l close parenthesis
09:24 Nion Enter.
09:26 Ki values jong x one bad x two la pyni.
09:30 Ki number jong ki iterations ban solve ia kajuh ka problem ki kham duna ban ia ka Jacobi method.
09:37 Solve ia kane ka problem da lade da kaba pyndonkam ia ka Jacobi bad Gauss Seidel methods.
09:43 Ha kane ka jinghikai, ngi la pule ban:
09:47 Develop ia ka Scilab code na ka bynta ban solve ia ka system jong ki linear equations.
09:52 Wad ia u value jong ki unknown variables jong ka system jong ki linear equations.
09:58 Peit ia ka video ba don ha ka link harum.
10:01 Ka batai kyllum ia ka Spoken Tutorial project.
10:04 Lada phim don ia ka bandwidth kaba biang, phi lah ban shu download bad peit ia ka.
10:09 Ka kynhun jong ka Spoken Tutorial Project
10:11 Ka pynlong ia ki workshops da kaba pyndonkam da ki spoken tutorials
10:15 Ka ai certificates sha kito kiba pass ha ka online test.
10:18 Na ka bynta kham bun ki jingtip ba bniah, sngewbha thoh sha ka contact@spoken-tutorial.org .
10:25 Spoken Tutorial Project kadei shi bynta jong ka Talk to a Teacher project.
10:30 La kyrshan ia ka da ka National Mission on Eduction lyngba ka ICT, MHRD, Sorkar India.
10:37 Kham bun ki jingtip halor kane ka mission kidon ha http://spoken-tutorial.org/NMEICT-Intro.
10:49 Nga i Meboreen na Shillong, nga pynkut ia kane.
10:51 Khublei Shibun ia ka jingsnohkti lang jong phi.

Contributors and Content Editors

Meboreen Mary