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SQP algorithms for solving Toeplitz matrix approximation problem. (English) Zbl 1071.65081
The following problem is considered: Given an \(n \times n\) matrix \(F\) and a natural number \(m \leq n\), find an \(n \times n\) symmetric positive semi-definite Toeplitz matrix \(T\) that minimizes the distance \(\| F-T \| \) in the Frobenius norm and whose rank is equal to \(m\). By means of a block \(LDL^{\text{T}}\) factorization of \(T\), the problem is reformulated, i.e., constraints put on \(T\) are transformed into a simpler form. Then, an SQP-based algorithm is presented and illustrated by numerical examples.

MSC:
65K05 Numerical mathematical programming methods
90C90 Applications of mathematical programming
90C55 Methods of successive quadratic programming type
Software:
filterSQP
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References:
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