represents the Cauchy matrix given by the generating vectors x and y as a structured array.
converts a Cauchy matrix cmat to a structured array.
Details and Options
- Cauchy matrices, when represented as structured arrays, allow for efficient storage and more efficient operations, including Det, Inverse and LinearSolve.
- Cauchy matrices occur in computations related to rational interpolation, conformal mappings, n-body simulations and the discretization of integral equations with singular kernels.
- Given generating vectors x and y, the resulting Cauchy matrix has entries given by .
- Operations that are accelerated for CauchyMatrix include:
Det time Inverse time LinearSolve time
- For a CauchyMatrix sa, the following properties "prop" can be accessed as sa["prop"]:
"XVector" generating vector x "YVector" generating vector y "Properties" list of supported properties "Structure" type of structured array "StructuredData" internal data stored by the structured array "StructuredAlgorithms" list of functions with special methods for the structured array "Summary" summary information, represented as a Dataset
- Normal[CauchyMatrix[x]] gives the Cauchy matrix as an ordinary matrix.
- CauchyMatrix[…,TargetStructure->struct] returns the Cauchy matrix in the format specified by struct. Possible settings include:
Automatic automatically choose the representation returned "Dense" represent the matrix as a dense matrix "Structured" represent the matrix as a structured array
- CauchyMatrix[…,TargetStructureAutomatic] is equivalent to CauchyMatrix[…,TargetStructure"Structured"].
Examplesopen allclose all
Basic Examples (2)
CauchyMatrix objects include properties that give information about the array:
When appropriate, structured algorithms return another CauchyMatrix object:
The transpose is also a CauchyMatrix:
Represent the Hilbert matrix as a CauchyMatrix:
Compare with HilbertMatrix:
Use CauchyMatrix to compute the coefficients for an interpolating rational function with fixed poles:
Define the Parter matrix as a CauchyMatrix:
Properties & Relations (2)
Possible Issues (3)
Wolfram Research (2022), CauchyMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/CauchyMatrix.html (updated 2023).
Wolfram Language. 2022. "CauchyMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/CauchyMatrix.html.
Wolfram Language. (2022). CauchyMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CauchyMatrix.html