Mathematical Computing - Science topic

Sure dear professor

There are many reasons why your forecasts may appear to be linear rather than capturing the expected seasonal patterns. One possible reason is that the model you are using is not appropriate for the data you are working with. Another possible reason is that you have not included all of the relevant variables in your model.

There are several open-source software and applications that you can use to write your mathematical model equations and automatically calculate the measurable inputs as they are keyed in. Here are a few options:

These are just a few examples, there are many other options available. It depends on the specific requirements of your project and your personal preference.

Fakes are everywhere these days.

I think the best way is to use the results of the semantic segmentation and samples of leaves from fieldwork to create your mathematical expression using any curve fitting mathematical tool.

Mohamed Elhadad Than you for your answer

The phase shift we wish to get here can be defined in this example, where two signals x(t) and y(t) are generated using real valued functions, and the phase shift between the two signals are calculated using Fast Fourier Transformation (FFT) method.

eg. A minimal coding example to get phase shift:

x = 2 + cos(2*Pi*f*t) + noise, y = 1/x

X = FFT(x), Y = FFT(y)

delta phi = angle(X*conj(Y))

Where f is the signal oscillation frequency, t is time axis. Function angle() to get the argument (phase) of complex value. Function conj() to get the conjecture of complex value.

Dear Ait Mansour El Houssain

By trying to answer your question I found the following reference with many examples on how the zeta functions (the reference doesn´t call it Riemann z functions) are all related in a natural way to eigenvalues of specific boundary value problems.

In statistical physics Z Riemann function is found in:

without sin, sinh and tanh

y = 22.1343029549693 + 10.8292764965611*x + 0.296189687976693*x*z^2 + 27*z/x^2 - 2.11016161227361*x*z - 0.270179597887278*x^2

This

https://docs.mosek.com/modeling-cookbook/index.html

also provide a lot of information for how to convert a convex problem to conic form e.g. second order cone form. This should be your best option as mentioned by Adam Letchford. Mosek is of course one among several optimizers for SOCPs.

International Journal of Applied Mathematics and Computer Science

Language English

Edited byJózef Korbicz

Publication details

Former name(s)Applied Mathematics and Computer Science

Publication history 1991-present

Publisher University of Zielona Góra and Lubuskie Scientific Society (Poland)

Frequency Quarterly

Open access Yes

Impact factor (2016)1.420 Standard abbreviations ISO 4 Int. J. Appl. Math. Comput. Sci.Math Sci Net Internat. J. Appl. Sci. Comput.

Indexing

ISSN 1641-876X (print) 2083-8492 (web) OCLC no.54678624 Links

Yes Roberto Ferretti , I have done that by using Matlab.

Hey there,

You can find interesting topics, related to artificial intelligence, in "https://www.quora.com/What-are-the-hot-topics-in-artificial-intelligence-for-research". In general, neural networks (in particular, convolutional neural networks) have received many efforts of the research community, therefore, this is an important/relevant topic.

There is no such methodology used in developing unbreakable codes, I guess.

Its a trade off between matrix dimension and sparsity. Often, FEM methods have large but sparse matrices, whilst RBFs tend to involve smaller but less well conditioned metric matrices. Progress on ill-conditioning of RBF kernel matrices is partially overcome by Mercer expansion of the GRBF. See Fornberg & co, as well as Fasshauer and McCourt.

I believe that, we can use it the physics laboratory and engineering laboratory to make the data experiments and Mathematics equations after that solving mathematically, so you can use it ta the class for more interesting during the lecture.

regards

Actually, I don't think it is the case that mathematicians don't like evolutionary algorithms.  I think what mathematicians really don't like is the way that some researchers claim to come up with "new" meta-heuristics every month or two, based on things like bats, fireflies and water droplets.  Very good discussions of this phenomenon can be found in the following papers.

20

Thanks Viera answer I've got that the proof for even  n  is quite sufficient. Thank you Viera for keeping calm while giving interesting answers to interesting questions:)

Best regards, Joachim

PS. Meanwhile I have realized, that replacing   a_k²  by  c_k  and and assuming increasing ordering (without losses, as Viera has noticed) , we are getting for the sum S of the question the following expression with the use of divided difference of order  n-1:

               (n-1)! (-1)^n-1 S = (n-1)! [ c₁, c₂, . . . , c_n :  f(c) ], 

which equals the value   f^(n-1)(b)  of the derivative  of  f  of  order  n-1  at some point  b  from [c₁ ,  c_n ],  where  in this case   f(c) = 1/\sqrt{c}.

  For the calculus of divided differences and their reprepresentation see e.g.

Having this and the sign changes of the derivative of the inverse square root one gets positive value of   S, for any choice of   positive   c_k -s .

Further conclusion is the  this holds for every negative power of  c  put in place of  f(c),  and also for every Laplace transform  of a positive measure on  R₊  since then the derivatives of order  n  have  sign equal   (-1)ⁿ  (cf. the William Feller Bible on probability about the completely monotone functions)  JoD

I think yes. It provides a convenient analytic tool to solve many nonlinear ordinary differential equations  as well as some nonlinear partial differential equations.

Dear Patrick, thank you. Apparently, I was concentrated on the first sentence of the question, and did not pay attention to the last one.

Right, Mr Ravi.Homotopy methods use a real valued embedding parameter on a convex trajectory and traverse from a easy solution to the real and more difficult solution. 

The other similar method is holomorphic embedding with a complex parameter, also used foe loadflow studies. 

My doubt is: Is the homotopy method a special case of holomorphic method. What special advantage, if any, does the holomorphic method has over homotopy method?

G K Rao

module matrix(clk,rst,a00,a01,a02,a03,a10,a11,a12,a13,a20,a21,a22,a23,a30,a31,a32,a33,b0,b1,b2,b3,c0,c1,c2,c3,p,t);

parameter s0=3'b000,s1=3'b001,s2=3'b010,s3=3'b011,s4=3'b100,s5=3'b101,s6=3'b110,s7=3'b111;

input clk,rst;

input [6:0] a00,a01,a02,a03,a10,a11,a12,a13,a20,a21,a22,a23,a30,a31,a32,a33;

input [6:0] b0,b1,b2,b3;

output reg [17:0] c0,c1,c2,c3;

output reg [17:0]p,t;

reg[17:0] q,r,s;

reg [3:0] count,count1;

reg [2:0] state,next_state;

/*initial

begin

p=18'd0;

q=18'd0;

r=18'd0;

s=18'd0;

c0=18'd0;

c1=18'd0;

c2=18'd0;

c2=18'd0;

end*/

always@(posedge clk)

begin

if (rst)

count<=4'd0;

else if (count==4'd7)

count<=4'd0;

else

count<=count+1;

end

always@(posedge clk)

begin

if(rst==1'b1)

state<=s0;

else

state<=next_state;

end

always@(state)

begin

case(state)

s0:

begin

p=a00*b0;

next_state=s1;

end

s1:

begin

p=p+(a01*b1);

q=a10*b0;

next_state=s2;

end

s2:

begin

p=p+(a02*b2);

q=q+(a11*b1);

r=a20*b0;

next_state=s3;

end

s3:

begin

p=p+(a03*b3);

q=q+(a12*b2);

r=r+(a21*b1);

s=a30*b0;

c0=p;

next_state=s4;

end

s4:

begin

q=q+(a13*b3);

r=r+(a22*b2);

s=s+(a31*b1);

c1=q;

next_state=s5;

end

s5:

begin

r=r+(a23*b3);

s=s+(a32*b2);

c2=r;

next_state=s6;

end

s6:

begin

s=s+(a33*b3);

c3=s;

next_state=s0;

end

default:

begin

next_state=s0;

end

endcase

end

@Latrache - In given PDE solution, we can consider x and y points are two matrix values?

e^(-t+i*pi))=-e^(-t)

e^(-t-i*pi))=-e^(-t)

Ei(z) = - Integral from (-z) to infinity of (e^(-t+i*pi))/(t-i*pi) dt=

= Integral from (-z) to infinity of (e^(-t))*(t+i*pi)/(t^2+pi^2) dt=

=Integral from (-z) to infinity of (e^(-t))*t/(t^2+pi^2) dt+

+i*Integral from (-z) to infinity of (e^(-t))*pi/(t^2+pi^2) dt

Okay Hans,

Kind regards, florian

Thank you very much for your answer!

Our library has this book, I will try to get it this afternoon. I read about the MatLAB codes, but tried to solve the problem solely with Abaqus to reduce complexity. As this does not work, I guess MatLAB should be the easiest solution then, I will check it out. Thank you again for your input!

Best regards

Rene Moitroux

 Thank you, Professor Michael.

An excellent book is:

Partial Differential Equations by Lawrence C. Evans, Graduate Studies in Mathematics, Volume 19, American Mathematical Society, Rhode Island (1998). This is a very readable textbook, that is also highly estimated by some of my colleagues in mathematics. Warning: Results on the existence of global (not only local) solutions are meagre.

There has been great emphasis in the literature on the derivation of well balanced schemes for the shallow water (SHW) and similar equations in the case in which both the continuity equation and the momentum equation are in full flux form. However, for many applications (especially in subcritical regimes), in my opinion,  there is no real necessity of employing the momentum equation in full flux form, since strict momentum conservation is often not really necessary (especially when dissipative terms are important and, as often happens, uncertain). In these cases the pressure gradient term is best written in non conservative form (see e.g. what is done in this paper

Rosatti, G., Bonaventura, L., Deponti, A., & Garegnani, G. (2011). An accurate and efficient semi‐implicit method for section‐averaged free‐surface flow modelling. International Journal for Numerical Methods in Fluids, 65(4), 448-473,

but there are many others also doing this). If you do that, the well balancing property is essentially automatic and granted for free and you do not need to worry about which approach to choose. Going deeper into well balancing issues is only really necessary when strict momentum conservation is essential (for example, when solving dam break problems). However, you can see from the previous paper that good solution for dam break problems can also be achieved for SHW equations formulated as suggested above.

Dear Rajkamal Kumar,

I like your idea of diminishing the role of outstanding data, which is an especially important feature for measurements/observations exposed to extraordinary random perturbations. However, there are some places, where we cannot aply the term of the 'true' mean value, unless a particular model of the perturbation is assumed and then analysed. Seemingly, a simle and directly correponding to your idea example can be given as follows:

The statistical procedure measures a rv $X$ with pd being a convex combination of the PROPER pd (with pr. p) and the FALSE pd Q (with pr. q = 1- p), in symbols:

$P_X = p \cdot P + q \cdot Q$

Now, for being more specific, let both be normal

${\cal N}(m,v)$ and ${\cal N}(M,V)$, respectively,

where the expectations are different ( $m \ne M$ ) and with variances satisfying $0 < v << V $. I think, that simulations will show in this case better approximation of $m$ with your weighted mean that the usual arithmetic mean.

Best wishes and good luck in continuing the proposal.

PS. The following is a sketch of a reason to ASSUME, that Kumar's average $K(x)$ of $d$ entries

$ x = ( x_1, . . . x_d)$

takes value zero, at points, where at least one coordinate equals the arithmetic average, denoted further by $A(x)$:

0.The average $K$ is defined only for sequences where none coordinate equals the average $A(x)$.

1. For these $x$-s, denoting

$y_j := 1 / (x_j - A(x))$ and $\sum$ for $\sum_{j=1}^d $

we have horeover,

$

|K(x) - A(x)|

\le |(\sum_{j=1}^d y_j ) / ( \sum y_j^2 ) |

\le (\sum_{j=1}^d |y_j| ) / ( \sum y_j^2 )

\le ( \sum_{j=1}^d |y_j| ) / ( [ max{ |y_j| : over j} ]^2 )

\le ( d \cdot max{ |y_j| : over j} ) / ( [ max{ |y_j| : over j} ]^2 )

\le d \cdot [ min{ |x_j - A(x)| : over j} ]

$

Joachim Domsta

The textbooks  that I used when I was a student are in Russian, which I afraid make them of little use for you :).  I have made a google search with keyword ``existence and uniqueness of solution for linear differential equation'' and have found immediately the following text that contains the exact statement of the theorem and the reference  to a texbook:

It also contains the explanation, why in the homogeneous case there are n linearly independent solutions, that I sketched in my previous post, and what happens in the non- homogeneous case.

Another reference:

D. Willett.  The Existence-Uniqueness Theorem for an nth Order Linear Ordinary Differential Equation.  The American Mathematical Monthly

Vol. 75, No. 2 (Feb., 1968), pp. 174-178 

pls refere to the files

You need to understand the meaning of inverse and where it exists.

Dear Chittesh,

This is a good question with many possible answers and points-of-view.   It seems that it is often the case that we learn about human behaviour indirectly by considering how humans interact with other humans, the environment and machines.   In short, mathematical views of human behaviour often focus on stimulus-response modelling.

Mathematical models of human behaviour have been recently been studied in the context of epidemics in

P. Poletti, Human behaviour in epidemic modelling, Ph.D. thesis, University of Trento, 2010:

Human behaviour is modelled by Poletti in terms of two mutually influencing phenomena: epidemic transitions and behavioural changes in the population of susceptible individuals (see Section 2.2, starting on page 16).

Modelling human-computer (device) interaction is the focus of

P. Eslambolchilar, Making sense of interaction using a model-based approach, Ph.D. thesis, National University of Ireland, Maynooth, 2006:

See, for example, the probabilistic framework of a model-based behaviour system in Fig. 6.13, starting on page 182.

A bit less mathematical but still very interesting model of human behaviour in terms of human-made music is given in

A. Tidemann, A groovy virtual drummer: Learning by imitation using a self-organizing connectionist architecture, Ph.D. thesis, Norwegian University of Science and Technology, 209:

For an overview of the Tidemann's approach to model and imitate human musical expressiveness, see Fig. 1.1, p. 5.

This thesis introduces the SHEILA architecture in terms of human drum-playing patterns with an accompanying melody (see Section 3, Architectuure, page 106 in the pdf file but unnumbered in the thesis).

(by James F Peters)

Consider also using a stepwise logistic regression in which you use 0=group 1 and 1=group 2, with twenty independent variables. If there is multicollinearity among the independent variables, it may be better to remove some variables before running the logistic regression. The odds ratio will tell you which variables are most important. 

Likewise have a look at the igraph package, in particular the graph.*.game  constructors for a graph.  In R you can just do install.packages("igraph")  library(igraph) and then ??graph to see various ways to construct graphs. 

See, for instance,

- Bard, Y. "Nonlinear Parameter Estimation". Academic Press, 1974

- Seber, G. A. F. & Wild, C. J. "Nonlinear Regression". Wiley-Interscience, 2003,  Section 7.5

- http://wiki.webpopix.org/index.php/Stochastic_differential_equations_based_models

Generally to get the frequencies VASP calculates the total energy after moving all atoms in space by a small step +-dx in 3D. From this VASP generates the hessian second derivative matrix of total energy with respect to atomic coordinates (with a finite difference scheme, but depending on the option you used in the INCAR), at the wanted configuration, and the eigenvalues are the frequencies. Since you have 120 atoms in the cell, at NFREE=2, this is 120*2*3=720 DFT calculations, which should converge separately, each with 120 atoms, which is what is taking so long. 

You can try to make this go faster by various ways, like reducing the convergence criteria, the kgrid density, and also by using selective dynamics on only part of the atoms if you don't need them all (say only near the surface if this is the case). There are many other ways of course.

If you want to salvage some of the data that was lost, you should check the OUTCAR, VASP should write there the energies at each configuration before the calculations was killed(depending on your INCAR input for NWRITE). You can then set selective dynamics off for the atoms that the calculation finished previously, and do the next calculation with only the missing atoms with seelctive dynamics turned on. From there you could construct your own hessian by a similar finite difference scheme and diagonalize it, instead of letting VASP do this.

Hope this helps,

Ofer.

In any textbook or lecture notes on the subject, e.g. http://www-fp.usc.es/~edels/SUSY/ (suffices to search for sqcd wz gauge and sort out the relevant entries).

This is an interesting question.

For very  recent consideration of incomplete hypercubes, see Section 4 in

and Section 3 in

@Abdelrahiem Ahmed Hashem: I too agree to all ..there is absolutely no reason for canny to not work if sobel and prewitt work in your system (I mean by chance if the edge code is not corrupt or overwritten in your system).. Would u mind sharing the error plz?

Thank you all for your replies.

thanks for your answer sir,

i also want to know , is it always necessary to calculate dissociation energy using various models like NEB or Drag and drop in Finding minimum energy path ? 

Dear Cooper

This book is useful in mathematica

www.springer.com/cda/content/.../cda.../9783540402459-c1.pdf?

In the particular case when the distance is attained, mentioned above, the hyperplanes H_1, H_2 are tangent  respectively to the boundaries of A, B at the points where the distance d(A,B) is attained.

maple will help you , coefftayl

I write for you example I expand the function sin(x+y) in taylor about (0,0) and I find the coefficient of x, y ,x^2y, xy^2,

restart:

f:=(x,y)-> sin(x+y);

e:=mtaylor(f(x,y), [x, y], 8);

coeftayl(e, [x, y] = [0, 0], [1, 0]);

coeftayl(e, [x, y] = [0, 0], [0, 1]);

coeftayl(e, [x, y] = [0, 0], [1, 1]);

coeftayl(e, [x, y] = [0, 0], [2, 1]);

coeftayl(e, [x, y] = [0, 0], [1, 2]);

coeftayl(e, [x, y] = [0, 0], [2, 2]);

Generate the matrix A as a sparse matrix in Matlab. If it's banded, you only need to generate the diagonals as vectors in order to create the matrix using the spdiags  command.

Then generate the right-hand side B, and solve by the usual x = A\B.

A 3000x3000 system is not particularly large, and the problem should be solved literally within seconds.

I think here is something good:

Alternating direction implicit is a splitting method based on treating terms coming from the discretization of spatial derivatives one at the time. It does not matter whether the coefficients are constant or functions of space and time as well. The main issue, from a modern perspective, is that the computational gains which made ADI popular 30 years ago are nowadays considered to be insufficient to justify the introduction of directional splitting error that results from using this method. I do not recall any relevant paper in CFD using ADI in the last 10 or 15 years. Conclusion: use any implicit method you want for time discretization, but solve the resulting linear/nonlinear system as it is, without introducing directional splitting by trying to reduce it to one dimensional problems.

Hi,

you can also have a look into this classic:

And if you like it faster, you can look into the sources and paper from this nice piece of code:

For periodic functions integrated over a period (as when computing the coefficients of a Fourier series) the midpoint and the trapezoidal rule coincide. These formulas can be proven to be superconvergent in this specific case, which means that for this special kind of definite integral, rather than being just second order accurate they are convergent of arbitrarily high order for functions that are C^infinity. Also for this reason, the discrete Fourier coefficients are defined by the application of the trapezoidal rule to the definite integral that defines the Fourier coefficient: there is no need of more accurate integration formulae, and on top of that Fast Fourier Transform algorithm apply for this definition of the discrete Fourier coefficients.

You can find more details in several books, see e.g.

Your problem is solved in more general case in the attached file by using "Shooting method". It might have useful to solve your problem by "Difference method".  

There is an authorative answer to your question.  The paper

Wen-Wei Lin, Volker Mehrmann, and Hongguo Xu, Canonical forms for Hamiltonian and symplectic matrices and pencils. Linear Algebra and its Applications, Volume 302-303, pages 469--533, 199, doi:  http://dx.doi.org/10.1016/S0024-3795(99)00191-3

provides the sufficient and necessary conditions under which the Hamiltonian Jordan form exists.  There is a vast literature on related questions in the (Numerical) Linear Algebra and Matrix Theory literature.

NOTE: the transformation to diagonal or Jordan form should only be used for theoretical purposes, never, never do it on a computer!  The transformation will be - unlike for symmetric matrices - be very ill-conditioned and will destroy the numerical accuracy of any computations!  For numerical purposes, there are other symplectic (orthogonal) transformations that should be used to simplify linear Hamiltonian systems! There is a recent survey on these, see

Angelika Bunse-Gerstner, Heike Faßbender, Breaking Van Loan’s Curse: A Quest for Structure-Preserving Algorithms for Dense Structured Eigenvalue Problems, In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Part I, pp. 3-23, Springer International Publishing, 2015.

DOI: 10.1007/978-3-319-15260-8_1

Both analytical and simulation methods are modelling approaches which aim at providing an idea of system performance, in different conditions.

An analytic model is a mathematical abstraction that can be extended to address various working conditions, thanks to some assumptions about the way a process is evolving. In some cases, an exact solution can be derived and a result can be obtained in various conditions. The beauty of the analytical model is that it provides a generic way to get performance results in various conditions through a mathematical formulation. The accuracy of the model is to be considered through the alidity of the assumption to derive the mathematical formulation. Some uncertainties can be handled through a stochastic model to account for modelling and measurement model.

A simulation model such as a monte-carlo also make assumption of a model and some assumption about the behaviour of the process. It is used when an analytical formulation cannot be derived (for example when the size of the model is too large,or when no exact solution can be derived). Simulation models provide results for a specific use case and should be run many times to counterbalance the effect of numerical calculations. For a different functioning use case, the simulation should be run over again. A simulation model can be accepted when results are validated in  a number of working conditions under various input assumptions.

When the two approaches can be used, preference should be given to the analytical approach and simultation can be used to validate the assumptions and the models. For better analysis, the simultaion model could be used with assumptions slightly different from the analytical model, since simultation is not aimed at validating the model but the reality of the modelled process.

For curved surface there is no projection. But there is a point (points) at the surface at the small distance from the initial poyint. It is the standard variational problem (conditional minimum) 

Cuda processors are SIMD (single instruction multiple data) architectures. Cuda processors are extremely efficient at computation on data that is not dependent on one another. Depending on the algorithm several dependencies may arise that give way to a break in parallelism.This break in parallelism usually takes place through conditionals.

You would need to be specific on the algorithm to get a more specific answer, since integration could benefit from reduction operations in CUDA, but again it depends on the algorithm.

Following the definition for exp^A, it exists only A is a square matrix (V. I. Arnold, ODE, M, 1971, p 92). In Your case A is a (m,n) matrix, m<n, x is a matrix or a vector of the type (n,1) , then Ax is a matrix of the type (m,1), i. e. non - square matrix. I will repeat the words of prof. Reza Zomorrodian : Please let me know if I did help or is this a new study that I am not aware of. Your sincerely: Anna Tomova

Dear A. H. Bhrawy,

                              I think you may better know about it . But if we implement Laguerre polynomials together with operational matrices of integration and differentiation we will easily convert the problem to system of algebric equations. 

If you are also interested in the theoretical point of view, you may want to look at this paper DOI: 10.1002/cpa.21453. This work was mainly motivated by the so called hybrid inverse problems. You can find similar problems and techniques from my contribution page.

Your question is not completely clear. Do you mean you are looking for a set-valued map that is not the subdifferential of a function, the word "subdifferential" being taken in one of the existing meanings given by a list of properties?

The application you have in view seem to orient to another interpretation.

It generally can do that. There may be a limitation due to the specific implementation that you are using, but there should be no reason that the GA cannot do this.

Very strange, first the gf then the object to count!

That is straightforward. A finite element model is needed.

Afterwards you can compare the load deflection curve of your experimental setup with your numerical simulation.

In principle it is possible to nondimensionalise any number of ordinary differential equations, but this rapidly becomes less useful as the number of equations becomes larger.

For the (linear) equation of a damped pendulum with displacement, time and (say) three physical coefficients, time and displacement can be scaled  to get an equation with one dimensionless parameter, say gamma, which determines whether the equation is under-, over- or critically damped.

If you had three or four equations for three or four coupled pendulums, in principle you still have a lot of dimensionless parameters after you scale  time and the displacements. This still gives you a large parameter space and very complicated, possibly chaotic behaviour, unless you are able to make simplifying assumptions and set some parameters to zero.

not all data attributes  require discretization

so many classifiers can be used on such raw data

decision tree algorithms very often use a built-in default discretization  alg. not visible to the user

I did

SetPrecision[Log10[Pi], 1000000]

in Mathematica10 and 4 seconds later I had many screens full of digits, the last three of them being 435.

Does this have some relation with elasto-plasticity?

Tsallis is still in use , Shanon is used for comparison. Many papers show work on Renyi and Kernel entropy based methods.

I guess that you are aware that you can compute the integral analytically, so the first numerical method would be a difference of function evaluations at the endpoints.

Apart from that:

If you want to do it in a purely numerical way, you might want to start with a composite trapezoidal integration just for a start to get a feeling what numerical integration is about.

You can also try higher Newton-Côtes formulas to see what differences in error order mean, and the Newton-Côtes formulae are still easy to implement.

As the final method, you should use Gauß-Laguerre integration, since it will compute the exact result of your integral, already with a 1st order formula.

Dear Milorad i used T-Tecto software to calculate the paleo stress but i still confused how to used the parameter in the paleo stress, i have only thrust fault (Azmuthe , dip, lineation , direction of the fault (scene) when i try to compute it i found difficulty to used the parameter in the inverse analysis i mean the best parameter for my data like (Parameter s ,Parameter d , Parameter q1 , Parameter q2, Stress parameter, Supposed dispersions, Inversion methods,) and other parameter i try with different input and in everytime i get result so i will appreciate your helpfull

thank

Thank you for your help

What is your metric for "fast". Time complexity or experimental results? That may help researchers answer your question.