Tridiagonal Systems in MATLAB | @MATLABHelper Numerical Methods

0:00 Introduction
0:08 Understanding Tridiagonal Systems
1:50 MATLAB code to implement Tridiagonal Systems

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[MATLABHelper]

0:00 Introduction
0:08 Understanding Tridiagonal Systems
1:50 MATLAB code to implement Tridiagonal Systems

[archit.saxena]

We often encounter #tridiagonal matrices in statistical physics, quantum mechanics and rotational physics as well. This video explains the definition precisely and with brevity.
Being able to work out a MATLAB code to solve tridiagonal systems is very useful and comes handy.

[HarpreetSingh-xpss]

Overall the video explains the concept properly with a brief introduction. a little modification can be added (like explanation of the syntax of the for loop)
Apart from this video editing is just great and it is easy for a learner to learn the concept with that good video editing and the soundtrack which does not make you feel bored.

[anishgupta]

#Triangle_Diagonal_Matrix is a matrix with a band of only 3 elements in each row rest all elements are 0. In tutorial the sub & super diagonal elements are made as -1 and then solved. We can also use #Thomas algorithm to solve tri-diagonal system which converts the band into 2 element form where diagonal elements are made as 1 and super diagonal matrix is put up for calculation.
As for loop it will be there depending on number of rows in the matrix, if it is small loop can be avoided too.
Thanks for the explanation.

[dishanikam]

System has #bandwidth of three.Consider, f=#diagonal vectors, e=#subdiagonal vectors, g=#superdiagonal vectors, r=#right hand side vectors.In first step we have to define function x=#tridiag(e, f, g, r).Where x is a #solution vector.Define n as length of f i.e. #n=length(f).Uses #forward elimination and then #back substitution.It uses #fprintf() function to print the value.

[bhagyakasam]

Clear explanation i got little idea about this

[DrSTM]

Very clear .. very useful .. Many thanks for this great explanation

[pushpagautam]

Dear sir, this video is really good to understand theory. I followed the MATLAB code exactly as you did but after the last step instead of output the computer says "undefined function 'Tridiag' for input arguments of type 'double' " .So how can I solve the problem? I am hoping you will help me.

[rajasekargopalsamy]

These type of Matrices are called #Banded matrics. They come across many application #for eg: Central difference method in Finite Difference Method. Special algorithms can be written for Banded Matrices to save time and memory space in solving such systems. #These special algorithms basically rely on making use of the memory space occupied by zeros. #Tridiagonal Matrices are Banded matrices with #bandwidth =3 and semi bandwidth =1

[yemmeprasanna]

Thanks for this video. I got some idea about it after watching this.

[sibasishdhibar]

Sir how to solve tridiagonal but the tridiagonal matrix is in the form of block matrix???

[bharathbharadwaj]

I got a small idea about it !! But without using #for loop !! Can we have another type to program this!!

[sibasishdhibar]

hello, sir how to solve the Tridiagonal block matrix for finite matrix???

[XclusiVvHD]

Can I get an explanation for the formula for f2 and r2?

[RavindraKempaiah]

Hi there,
I keep getting this error. Could you please help?

Error in GaussCubicSpline (line 10)
n=length(f);

[arathireddyb]

The problem given is nice intresting topic

[zengalex]

Hey! Can you please explain why vector e starts with 0?

[dynamicdonut]

I followed every step, but I get an "index exceeds the number of array elements" error and an error in line 17 :/

[ASHISHPATEL-nuig]

i tried to solve a 6x6 Tridiagonal matrix it results in error.

[someshwararnoorla]

you forgot to change the g values in the first loop