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0
votes
1answer
62 views

Block matrix and calculate it's inverse

How to define the following block matrix $$ A=\begin{bmatrix} H-G_1 & -G_1 & \ldots & -G_1 \\ -G_2 & H-G_2 & \ldots & -G_2 \\ \vdots & \ldots & \vdots & \vdots ...
1
vote
1answer
79 views

Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?

Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, ...
1
vote
1answer
98 views

In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
1
vote
1answer
60 views

Fit to inverse function

I am trying to fit my data to an inverse function from solving a DGL: ...
2
votes
1answer
66 views

Inverse error function

I solved some equation in Mathematica and I obtained something like $$y(t)=\exp \left\lbrace \left[ \text{erf}^{-1} (\text{i}t) \right]^2\right\rbrace, (1)$$ where $\text{i}$ is imaginary unit and ...
4
votes
1answer
127 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...
3
votes
2answers
225 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
0
votes
2answers
39 views

Taking inverse powers of an expression to that power [closed]

I'm finding a curious behavior for Mathematica 8. The code (x^3)^(1/3) does not want to Simplify or FullSimplify. I'd prefer not to make a rule for this, because ...
1
vote
1answer
111 views

Inverting matrix of unknown size

I have a matrix that has a variable number of columns and rows (but it is always square). The matrix is: $$ \Gamma = \begin{bmatrix} \Theta & 0 & 0 & 0 & T & 0 & R_j \\ ...
0
votes
1answer
131 views

Inverse of a restriction of a non-invertible matrix

Let $A∈R^{4×4}$ be a non-invertible matrix, with $2$-dimensional kernel. How can I compute the inverse of the restriction of $A$ on a subspace where it is invertible: $A^{-1}v \,\,\,\,$ where ...
0
votes
1answer
59 views

Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). ...
0
votes
1answer
175 views

Specific entry of inverse of large matrix

Given a large (say 10x10) sparse Hermitian matrix with symbolic entries, I need four specific entries of the inverse matrix. It seems wasteful to me to compute 100 entries of which I only need a few ...
0
votes
1answer
54 views

inverting this equation [closed]

I'm trying to inverse this equation Z = X + X^2 / 2 but couldn't wrap up my head around it. If anyone can provide a step by step solution to this it will be ...
0
votes
1answer
548 views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
0
votes
0answers
148 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
0
votes
0answers
32 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
1
vote
1answer
140 views

invert system of two parametric ODEs and plot results of do-loop

I can solve this system of parametric ODE (u is the parameter,while g,e and ...
1
vote
1answer
158 views

How to do Inverse formulas/Rearrange formulas in Mathematica? [duplicate]

Hi am a student in chemical engineering and I have the necessity to rearrange formulas algebraically, for example ...
1
vote
0answers
131 views

Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere ...
0
votes
1answer
110 views

Finding the InverseFunction of a polynomial function restricted to an interval [duplicate]

I want to calculate the inverse of f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2 f[x] is monotonic inside ...
5
votes
0answers
42 views

InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
0
votes
0answers
139 views

Calculating Second-Order Tikhonov Regularization Parameter in Mathematica

I am trying to map slowness of underwater sound velocity in a river using some tomographic device. The location of each acoustic receiver/transmitter is shown in the picture below To find the ...
8
votes
2answers
273 views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
0
votes
0answers
256 views

Invert Colors Stylesheet White on Black

There have been a couple studies done that showed that white text on a black background increase recall of data. Although this is certainly debatable how might I invert the colors of Notebook font ...
7
votes
1answer
89 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
2
votes
1answer
199 views

Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f = Piecewise[{{Exp[-β * (-Log[#])^α], 0 < # <= 1}}, #]& with ...
4
votes
1answer
334 views

InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
1
vote
1answer
410 views

Prandtl-Meyer function

I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error. Here is my code: ...
3
votes
5answers
925 views

Plotting the solutions to a transcendental equation

I am trying, to no avail, to use Mathematica to produce a plot in (x, y)-space of the solutions to the equation Cos[Sqrt[y]] + Sin[Sqrt[y]]/Sqrt[y] == Cos[x] ...
4
votes
1answer
491 views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
3
votes
1answer
376 views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
1
vote
0answers
218 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
3
votes
3answers
674 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
2
votes
1answer
518 views
3
votes
2answers
3k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
7
votes
0answers
546 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
7
votes
2answers
3k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
6
votes
2answers
1k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
3
votes
3answers
937 views

Changing variables algebraically

Suppose one has two functions, $y(x)$ and $z(x)$, and one seeks to obtain $y(z)$ by substituting $x(z)$ into $y(x)$. Can this be done in a single step? Or must $z(x)$ first be inverted independently? ...
2
votes
1answer
1k views

Mathematica Can't Evaluate This?

I am trying to find the inverse function of $\frac{\ln{x}}{x^2}$ in Mathematica. I am using the Solve[] function to find the inverse (yes, I know about ...
18
votes
3answers
2k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...