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Approximate a numerical matrix as sum of Kronecker products
ResourceFunction["NearestKroneckerProductSum"][m,{p1,q1},{p2,q2},n] gives a decomposition of a numerical matrix m into a sum of n Kronecker products of matrices of dimensions p1×q1 and p2×q2. | |
ResourceFunction["NearestKroneckerProductSum"][m,{p1,q1},{p2,q2},UpTo[n]] gives the decomposition for n Kronecker products, or as many as are available. |
Compute a Kronecker product approximation of a small matrix:
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Form the approximant to the original matrix:
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Using two terms gives a much better approximant:
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The Frobenius norm of the remainder matrix is on the order of machine precision:
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Define a 10×12 matrix:
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Express the matrix as a sum of three Kronecker products of matrices of dimensions 5×3 and 2×4:
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Check the difference between the original matrix and the sum of the Kronecker products:
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A 10×12 matrix with approximate numerical values:
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Express the matrix as a sum of up to seven Kronecker products of matrices of dimensions 2×3 and 5×4:
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Check the difference between the original matrix and the sum of the Kronecker products:
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An arbitrary-precision 10×12 matrix:
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Express the matrix as a sum of up to seven Kronecker products of matrices of dimensions 2×3 and 5×4:
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Check the difference between the original matrix and the sum of the Kronecker products:
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Decompose a random complex-valued 10×12 matrix into a sum of two Kronecker products of matrices of dimensions 2×3 and 5×4:
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NearestKroneckerProductSum is left unevaluated for symbolic input:
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NearestKroneckerProductSum is left unevaluated for exact input:
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Numericize the input to get a result:
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NearestKroneckerProductSum is left unevaluated if the specified dimensions are incommensurate:
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The decomposition of a matrix into a sum of Kronecker products is not unique:
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