# Numerics

**URL:** https://discourse.julialang.org/c/domain/numerics/20.md?page=35

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**Page:** 36

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## [How could I define my own division operation with QR decomposition?](https://discourse.julialang.org/t/how-could-i-define-my-own-division-operation-with-qr-decomposition/26015)

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**Author:** [@Noel\_Araujo](https://discourse.julialang.org/u/Noel_Araujo)\
**Replies:** 0\
**Last updated:** [July 4, 2019, 4:28pm UTC](https://discourse.julialang.org/t/how-could-i-define-my-own-division-operation-with-qr-decomposition/26015 "2019-07-04T16:28:05Z")

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(Feel free to skip this part and look at the minimal example below) After a long time, I had to continue again with some old code, that stillyslalom already posted here, and because is a different question, I created a …

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## [Multivariable numerical integration with changing limits](https://discourse.julialang.org/t/multivariable-numerical-integration-with-changing-limits/25862)

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**Author:** [@sevimora](https://discourse.julialang.org/u/sevimora)\
**Replies:** 4\
**Last updated:** [July 2, 2019, 5:02pm UTC](https://discourse.julialang.org/t/multivariable-numerical-integration-with-changing-limits/25862 "2019-07-02T17:02:34Z")

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Hi! I am not very proficient in Julia (or in numerical methods, for that matter), so please be forgiving with my ignorance… I am trying to numerically integrate a function of the form: \\int\_a^b \\int\_{\\underline x(w)}…

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## [Inverse of a view of a symmetric matrix](https://discourse.julialang.org/t/inverse-of-a-view-of-a-symmetric-matrix/25877)

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**Author:** [@fipelle](https://discourse.julialang.org/u/fipelle)\
**Replies:** 3\
**Last updated:** [July 1, 2019, 1:35am UTC](https://discourse.julialang.org/t/inverse-of-a-view-of-a-symmetric-matrix/25877 "2019-07-01T01:35:09Z")

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Hi, I am trying to compute the inverse of a view of a symmetric matrix via: using LinearAlgebra V=Symmetric(rand(10,10)+50\*I); V\_view = @view V\[1:5,1:5\]; V\_view\_inv = inv(V\_view); However, it does not work and I get t…

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## [Speeding up sparse matrix multiplication and assembly](https://discourse.julialang.org/t/speeding-up-sparse-matrix-multiplication-and-assembly/25452)

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**Author:** [@thehalfspace](https://discourse.julialang.org/u/thehalfspace)\
**Replies:** 8\
**Last updated:** [June 24, 2019, 6:37pm UTC](https://discourse.julialang.org/t/speeding-up-sparse-matrix-multiplication-and-assembly/25452 "2019-06-24T18:37:47Z")

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I am trying to solve a large linear system using IterativeSolvers and AlgebraicMultigrid. Let my elemental stiffness matrix be Ke (size = 25x25xNe) where Ne is number of elements. The index for assembly is iglob (size =…

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## [Givens matrix for an integer vector](https://discourse.julialang.org/t/givens-matrix-for-an-integer-vector/25520)

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**Author:** [@zdenek\_hurak](https://discourse.julialang.org/u/zdenek_hurak)\
**Replies:** 6\
**Last updated:** [June 21, 2019, 2:23pm UTC](https://discourse.julialang.org/t/givens-matrix-for-an-integer-vector/25520 "2019-06-21T14:23:48Z")

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As a newcomer to Julia I am still struggling with various type-related issues. One of them is this: using LinearAlgebra julia\> x = \[3,4\] 2-element Array{Int64,1}: 3 4 julia\> G,r = givens(x,1,2) ERROR: MethodError: no…

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## [Montecarlo DAE](https://discourse.julialang.org/t/montecarlo-dae/25497)

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**Author:** [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Replies:** 4\
**Last updated:** [June 21, 2019, 7:21am UTC](https://discourse.julialang.org/t/montecarlo-dae/25497 "2019-06-21T07:21:54Z")

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Hi everyone - I am having a little problem defining a montecarlo DAE problem with varying parameters - Any help would be appreciated. Here is toy example, comparinng standard correct solution and montecarlo results. …

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## [Towards a common Manifold Framework / Package](https://discourse.julialang.org/t/towards-a-common-manifold-framework-package/24910)

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**Author:** [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Replies:** 10\
**Last updated:** [June 21, 2019, 7:13am UTC](https://discourse.julialang.org/t/towards-a-common-manifold-framework-package/24910 "2019-06-21T07:13:29Z")

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Continuing the discussion from \[ANN\] Manopt.jl I would like to collect Ideas and approaches towards a common package that should be the base for “Things on manifolds”: Solving optimization problems (disclaimer, I am deve…

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## [DAE with measurement type](https://discourse.julialang.org/t/dae-with-measurement-type/25281)

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**Author:** [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Replies:** 5\
**Last updated:** [June 14, 2019, 5:40pm UTC](https://discourse.julialang.org/t/dae-with-measurement-type/25281 "2019-06-14T17:40:29Z")

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Hi there I am running a complex set of differential equations and at some point it fails because of gemm!. The short story is that gemm! does not work with the meassurememnt type, and because the solver is calling gemm!…

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## [Explicit Jacobian on DAEs?](https://discourse.julialang.org/t/explicit-jacobian-on-daes/21477)

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**Author:** [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Replies:** 72\
**Last updated:** [June 13, 2019, 2:40am UTC](https://discourse.julialang.org/t/explicit-jacobian-on-daes/21477 "2019-06-13T02:40:38Z")

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Hello all, I am new to this forum I am somewhat confused on how to solve DAEs using the DifferentialEquations package - I am trying to solve a large system, that I think requires explicit Jacobian definition. I defin…

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## [DifferentialEquations.jl default options for a solver](https://discourse.julialang.org/t/differentialequations-jl-default-options-for-a-solver/19937)

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**Author:** [@michaelkyu](https://discourse.julialang.org/u/michaelkyu)\
**Replies:** 2\
**Last updated:** [June 13, 2019, 1:45am UTC](https://discourse.julialang.org/t/differentialequations-jl-default-options-for-a-solver/19937 "2019-06-13T01:45:54Z")

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In DifferentialEquations.jl, how can I find out the default options for a specific solver? In particular, I’d like to know the default options for the ODE solver DP5. I see a description of options in the docs, but I don…

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## [A faster pow(x,1/12) function available in Fast12thRoot.jl](https://discourse.julialang.org/t/a-faster-pow-x-1-12-function-available-in-fast12throot-jl/10893)

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**Author:** [@MrBelette](https://discourse.julialang.org/u/MrBelette)\
**Replies:** 12\
**Last updated:** [June 3, 2019, 1:47am UTC](https://discourse.julialang.org/t/a-faster-pow-x-1-12-function-available-in-fast12throot-jl/10893 "2019-06-03T01:47:13Z")

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New to Julia, so hopefully I’ve chosen the correct category for posting this. Actuaries use x^(1/12) very often in order to convert annualized numbers to their monthly compounded equivalent. I had an itch that had to be…

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## [Beginner - NumericalMath -- Use trapz routine and Number type](https://discourse.julialang.org/t/beginner-numericalmath-use-trapz-routine-and-number-type/24777)

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**Author:** [@fer](https://discourse.julialang.org/u/fer)\
**Replies:** 1\
**Last updated:** [May 30, 2019, 5:50pm UTC](https://discourse.julialang.org/t/beginner-numericalmath-use-trapz-routine-and-number-type/24777 "2019-05-30T17:50:17Z")

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It seems that NumericalMath.jl have some installation problems with julia 1.1.1 : here is my error message: \[ Info: Precompiling NumericalMath \[2d69212a-5df0-5a1f-8e4a-e8e814bdb11a\] ERROR: LoadError: LoadError: syntax: …

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## [Differential Equation Parameter Estimation Using Only A Subset of Variables](https://discourse.julialang.org/t/differential-equation-parameter-estimation-using-only-a-subset-of-variables/23423)

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**Author:** [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Replies:** 32\
**Last updated:** [May 30, 2019, 3:52pm UTC](https://discourse.julialang.org/t/differential-equation-parameter-estimation-using-only-a-subset-of-variables/23423 "2019-05-30T15:52:34Z")

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Hi, I have a DAE problem with 37 variables - I only have data for 12 of those variables - I would like to run parameter estimation with an L2Loss function based only on the 12 variables for which I actually have data. …

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## [Efficient QR factorization](https://discourse.julialang.org/t/efficient-qr-factorization/24767)

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**Author:** [@raphaelsaavedra](https://discourse.julialang.org/u/raphaelsaavedra)\
**Replies:** 3\
**Last updated:** [May 30, 2019, 2:49pm UTC](https://discourse.julialang.org/t/efficient-qr-factorization/24767 "2019-05-30T14:49:52Z")

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Hello, I’m having some issues with QR factorization in Julia 1.0. I want to efficiently compute the QR factorization of the transpose of a matrix and save only Q. Back in 0.6, there were LAPACK functions that did this e…

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## [Special method for finding eigenvalues of a large sparse symmetric matrix?](https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621)

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**Author:** [@406700](https://discourse.julialang.org/u/406700)\
**Replies:** 17\
**Last updated:** [May 29, 2019, 5:50pm UTC](https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621 "2019-05-29T17:50:37Z")

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Hi, I am looking to solve the eigenvalues of sparse symmetric matrix of ~ 14000x14000. Eigfact is too slow, and didn’t give results after an hour running. (8gb ram i7 processor) Are there special iteritive methods? …

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## [Shallow water equations with DifferentialEquations.jl](https://discourse.julialang.org/t/shallow-water-equations-with-differentialequations-jl/2691)

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**Author:** [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Replies:** 22\
**Last updated:** [May 24, 2019, 12:31am UTC](https://discourse.julialang.org/t/shallow-water-equations-with-differentialequations-jl/2691 "2019-05-24T00:31:41Z")

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I am really interested in using the DifferentialEquations.jl framework to solve the shallow water equations over a 2D domain efficiently instead of coding my own solution. How would you formulate the problem in Differen…

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## [PDE Solvers in Julia](https://discourse.julialang.org/t/pde-solvers-in-julia/24416)

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**Author:** [@xtalax](https://discourse.julialang.org/u/xtalax)\
**Replies:** 3\
**Last updated:** [May 21, 2019, 9:36am UTC](https://discourse.julialang.org/t/pde-solvers-in-julia/24416 "2019-05-21T09:36:13Z")

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Is there a Package that is able to solve PDEs in julia yet?

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## [Polynomial Roots With Multiplicities](https://discourse.julialang.org/t/polynomial-roots-with-multiplicities/24309)

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**Author:** [@Hans\_W\_Borchers](https://discourse.julialang.org/u/Hans_W_Borchers)\
**Replies:** 8\
**Last updated:** [May 18, 2019, 9:12pm UTC](https://discourse.julialang.org/t/polynomial-roots-with-multiplicities/24309 "2019-05-18T21:12:54Z")

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When using the roots function from the Polynomials package, the values found for multiple roots can be quite inaccurate. Just as an example, here is the polynomial with zeros at 1 and -1, each of multiplicity 4. julia\> …

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## [Is it possible to use BSplines to interpolate when scaling using collection of ranges](https://discourse.julialang.org/t/is-it-possible-to-use-bsplines-to-interpolate-when-scaling-using-collection-of-ranges/24125)

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**Author:** [@jints07](https://discourse.julialang.org/u/jints07)\
**Replies:** 2\
**Last updated:** [May 12, 2019, 2:55pm UTC](https://discourse.julialang.org/t/is-it-possible-to-use-bsplines-to-interpolate-when-scaling-using-collection-of-ranges/24125 "2019-05-12T14:55:10Z")

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I want to use scaled linear interpolation using BSplines with a 4-D matrix. One of the dimensions does not have all points equally spaced but is a 2 ranges put together. I read that BSplines are much faster than Gridded …

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## [How hard would it be to implement Numpy.jl, i.e. Numpy in Julia?](https://discourse.julialang.org/t/how-hard-would-it-be-to-implement-numpy-jl-i-e-numpy-in-julia/22080)

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**Author:** [@Pierre\_Augier](https://discourse.julialang.org/u/Pierre_Augier)\
**Replies:** 71\
**Last updated:** [May 9, 2019, 2:24pm UTC](https://discourse.julialang.org/t/how-hard-would-it-be-to-implement-numpy-jl-i-e-numpy-in-julia/22080 "2019-05-09T14:24:12Z")

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Hi, I’m working with Pythran (http://github.com/serge-sans-paille/pythran), a Python/Numpy to C++ transpiler, which of course supports only a subset of Python (in particular not all the crazy cool Python stuffs stupid f…

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## [Hessenberg factorization](https://discourse.julialang.org/t/hessenberg-factorization/20125)

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**Author:** [@olof3](https://discourse.julialang.org/u/olof3)\
**Replies:** 2\
**Last updated:** [April 27, 2019, 9:27pm UTC](https://discourse.julialang.org/t/hessenberg-factorization/20125 "2019-04-27T21:27:56Z")

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Hello, To compute the frequency response of a linear system \\dot{x} = Ax + Bu y = Cx where A is a square matrix, one should compute G(s) = C(sI - A)\\backslash B for several complex values s. This can be do…

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## [ForwardDiff errors when evaluating type: Array{Float64}](https://discourse.julialang.org/t/forwarddiff-errors-when-evaluating-type-array-float64/23361)

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**Author:** [@GregVernon](https://discourse.julialang.org/u/GregVernon)\
**Replies:** 2\
**Last updated:** [April 21, 2019, 5:31am UTC](https://discourse.julialang.org/t/forwarddiff-errors-when-evaluating-type-array-float64/23361 "2019-04-21T05:31:30Z")

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My questions are asked at the bottom of this post, but their background is developed through this post - which is perhaps a bit pedantic. I’m writing a p-method FEM code. Instead of explicitly coding high-order shape f…

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## [Signal (11): Segmentation fault: 11 with DifferentialEquations.jl](https://discourse.julialang.org/t/signal-11-segmentation-fault-11-with-differentialequations-jl/23264)

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**Author:** [@boutor2](https://discourse.julialang.org/u/boutor2)\
**Replies:** 2\
**Last updated:** [April 18, 2019, 11:22am UTC](https://discourse.julialang.org/t/signal-11-segmentation-fault-11-with-differentialequations-jl/23264 "2019-04-18T11:22:48Z")

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Hello there, It seems there is a bug with DifferentialEquations.jl when solving for large systems of ODEs. I tried to make the simplest example to obtain the error: using DifferentialEquations function f(du,u,p,t) …

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## [RFQ: InplaceLinalg](https://discourse.julialang.org/t/rfq-inplacelinalg/23195)

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**Author:** [@davidavdav](https://discourse.julialang.org/u/davidavdav)\
**Replies:** 9\
**Last updated:** [April 18, 2019, 11:49am UTC](https://discourse.julialang.org/t/rfq-inplacelinalg/23195 "2019-04-18T11:49:01Z")

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Hello, We’ve noticed that the broadcasting assignment operator .= does a good job in in-place assignment of the LHS in some cases, but not so in others. I suppose .= is really about broadcasting, and not about in-place…

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## [Treating Variable as Constant in ForwardDiff](https://discourse.julialang.org/t/treating-variable-as-constant-in-forwarddiff/23080)

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**Author:** [@mboutros](https://discourse.julialang.org/u/mboutros)\
**Replies:** 2\
**Last updated:** [April 12, 2019, 3:30pm UTC](https://discourse.julialang.org/t/treating-variable-as-constant-in-forwarddiff/23080 "2019-04-12T15:30:49Z")

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I’ve distilled my use case into a simple example. Essentially, I have an outer function that takes an input and generates a scalar from an inner function. I want ForwardDiff to treat this scalar as a constant when taking…

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## [Deval in solve](https://discourse.julialang.org/t/deval-in-solve/22873)

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**Author:** [@11110](https://discourse.julialang.org/u/11110)\
**Replies:** 1\
**Last updated:** [April 7, 2019, 2:45pm UTC](https://discourse.julialang.org/t/deval-in-solve/22873 "2019-04-07T14:45:04Z")

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Hello everyone! Is there a function similar to the one from Matlab deval in Julia? the deval function allows to find the value of the obtained solution trajectory at any point of the specified time interval after the pr…

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## [Defining custom matrix-free operators for solving a system of equations in iterativesolvers.jl](https://discourse.julialang.org/t/defining-custom-matrix-free-operators-for-solving-a-system-of-equations-in-iterativesolvers-jl/21150)

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**Author:** [@thehalfspace](https://discourse.julialang.org/u/thehalfspace)\
**Replies:** 5\
**Last updated:** [April 7, 2019, 10:20am UTC](https://discourse.julialang.org/t/defining-custom-matrix-free-operators-for-solving-a-system-of-equations-in-iterativesolvers-jl/21150 "2019-04-07T10:20:25Z")

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I am solving elastodynamic+elastostatic equations for waves and fracture using a spectral element method in 2D. One of the steps involves solving a large system of equations. I am currently using a preconditioned conjug…

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## [DifferentailEquations.jl error on multiple\_shooting\_objective](https://discourse.julialang.org/t/differentailequations-jl-error-on-multiple-shooting-objective/22387)

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**Author:** [@Andre\_Mello](https://discourse.julialang.org/u/Andre_Mello)\
**Replies:** 2\
**Last updated:** [April 5, 2019, 4:06pm UTC](https://discourse.julialang.org/t/differentailequations-jl-error-on-multiple-shooting-objective/22387 "2019-04-05T16:06:41Z")

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I’m still exploring the excellent DifferentialEquations.jl and came across this error today. I wanted to compare the different objective functions created by two\_stage\_method, build\_loss\_objective and multiple\_shooting\_…

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## [Request for comment: package for scientific and mathematical constants](https://discourse.julialang.org/t/request-for-comment-package-for-scientific-and-mathematical-constants/4155)

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**Author:** [@fasiha](https://discourse.julialang.org/u/fasiha)\
**Replies:** 31\
**Last updated:** [April 4, 2019, 10:16pm UTC](https://discourse.julialang.org/t/request-for-comment-package-for-scientific-and-mathematical-constants/4155 "2019-04-04T22:16:53Z")

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I’m refactoring some of our code and am wondering what to do with a few scientific constants we use, like speed of light, permittivity of free space, and the like. I was intrigued to see a stand-alone package, Tau.jl but…

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## [Updating lazy kronecker products](https://discourse.julialang.org/t/updating-lazy-kronecker-products/22650)

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**Author:** [@eliassno](https://discourse.julialang.org/u/eliassno)\
**Replies:** 4\
**Last updated:** [April 3, 2019, 1:22am UTC](https://discourse.julialang.org/t/updating-lazy-kronecker-products/22650 "2019-04-03T01:22:27Z")

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I need to calculate something of the form: where are dense matrices, are diagonal, is the identity matrix and is an arbitrary scalar function. The following code creates all the variations of Kronecker product…

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