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17
votes
3answers
2k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...
8
votes
2answers
167 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}}] ...
7
votes
2answers
2k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
7
votes
1answer
80 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 ...
7
votes
0answers
447 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
6
votes
2answers
976 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 ...
5
votes
0answers
33 views

InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
4
votes
1answer
341 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
5answers
682 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] ...
3
votes
3answers
530 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 ...
3
votes
2answers
2k 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) : ...
3
votes
1answer
257 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 ...
3
votes
3answers
685 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? ...
3
votes
1answer
176 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: ...
2
votes
1answer
890 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 ...
2
votes
1answer
416 views
1
vote
1answer
143 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 ...
1
vote
1answer
265 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: ...
1
vote
1answer
95 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
1answer
121 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
0answers
97 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 ...
1
vote
0answers
170 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 ...
0
votes
1answer
50 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
171 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
1answer
109 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
0answers
54 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
30 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 ...
0
votes
1answer
84 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 ...
0
votes
0answers
81 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 ...
0
votes
0answers
138 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 ...