## 60 Reputation

1 years, 283 days

## How do I store and retrieve the iterates...

Maple

Dear Maple community,

I'm trying to solve iteratively a system of (non-)linear equations and, to better understand the dynamics behind this process, would like to know the new/updated values of the unknowns after each iteration. Unfortunately, I wasn't able to implement this myself and was wondering whether you could give me hand?

Specifically, consider the following system of 4 non-linear equations in 4 unknowns: y[1], y[2], y[3], y[4]:

(EQ1): y[1]=f(y[1], y[2], y[3], y[4])

(EQ2): y[2]=f(y[1], y[2], y[3], y[4])

(EQ3): y[3]=f(y[1], y[2], y[3], y[4])

(EQ4): y[4]=f(y[1], y[2], y[3], y[4])

The goal is to set-up an iterative process along the following lines:

Step 1: Set the values of y[1] through y[4] on the right-hand side (RHS) equal to 1 and calculate the respective values of y[1] through y[4] on the left-hand side (LHS). Store the latter LHS values as {y[1]^0, y[2]^0, y[3]^0, y[4]^0}.

Step 2: Substitute {y[1]^0, y[2]^0, y[3]^0, y[4]^0} on the RHS, update the LHS values and store those as {y[1]^1, y[2]^1, y[3]^1, y[4]^1}.

Iterate Step 2 until convergence (which should yield the exact same result as with solving numerically the above system of 4 equations using the fsolve(.) command). Importantly, I would like to "retrieve" the values of each variable y[k]^i at each iteration i, where k=1,2,3,4, and i=0,1,... and use them for further analysis.

Iterative_solutionQ.mw

## How do I calculate all eigenvalues of a ...

Maple

Dear Maple community,
I've been trying to calculate all eigenvalues of a (large) symbolic matrix M (see EigenvaluesQ.mw) using:

```with(LinearAlgebra):
LinearAlgebra:-Eigenvalues(M):```

or simply

`Eigenvalues(M)`

but, unfortunately, my computer (64Gb RAM, Maple 2020) doesn't deliver a solution after 1 hour of computation. Am I doing something wrong? Thank you very much in advance!

## How do I calculate a Steady State Vector...

Maple 2020

Dear Maple community,

I'm trying to calculate a Steady State Vector of the attached matrix using this Maple routine, but, unfortunately, don't get any solution even after a 30 min calculation on a 64Gb machine. Am I doing something wrong and, if so, could you please give me a hand how to conduct this calculation? Thanks!

## How do I solve a system of non-linear eq...

Maple 2020

Dear Maple community,

I was wondering whether you could help me with the following problem: Consider the non-linear system of 4 equations in 4 unknowns: {y[2,1], y[2,2], y[4,1], y[4,2]}, see MapleQ.mw. Please also note that equations y[2,1] and y[2,2] in sys2 are homogenous of degree 1 (i.e., defined only up to scale). In principle, it should be possible to choose either y[2,1] or y[2,2] as a free and unconstrained variable (a scaling factor) and express all other unknowns in terms of it. Unfortunately, I couldn't yet implement it in the current setting and was wondering whether you give me a hand. Thank you very much in advance!

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## Issue with the calculation of (Moore-Pen...

Maple

Dear MaplePrimes community,

I'm trying to calculate the (Moore-Penrose) pseudoinverse of a matrix using the following code:

with(LinearAlgebra):
Identity := Matrix(2, 2, [[1, 0], [0, 1]]):
A := Matrix(2, 2, [[0.5661180126, 0.4338819876], [0.8316071431, 0.1683928571]]):
MatrixInverse(Identity - A, method = pseudo)

Unfortunately, the output appears to be meaningless (and it conincides with what I'm getting by calculating a simple matrix inverse using "MatrixInverse(Identity - A)"). Am I missing something? (And how do I calculate the (Moore-Penrose) pseudoinverse of the matrix (Identity-A)?)

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