From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation

Derevianko, Nadiia; Plonka, Gerlind; Petz, Markus

doi:10.1093/imanum/drab108

Cited by 17 publications

(27 citation statements)

References 34 publications

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“…Instead of applying an SVD of the matrix M N −L+2,L+1 in the first step of the algorithm 1, we can use also the QR decomposition of this matrix to improve numerical stability. This approach has been also employed for exponential sums, see [11,23,9] and is called matrix pencil method (MPM).…”

Section: The Arithmetical Complexity Of the Svd Decomposition Of The ...mentioning

confidence: 99%

“…Therefore, we shortly summarize this algorithm in our setting. For more detailed information we refer to [15,10] or to [9], where we have applied this algorithm for the recovery of complex exponential sums. The AAA algorithm is numerically stable due to an iterative procedure using adaptively chosen interpolation sets and a barycentric representation of the rational interpolant.…”

Section: The Aaa Algorithm For Rational Approximationmentioning

confidence: 99%

“…The problem is closely related with the recovery of and approximation by sums of exponentials of the form 2M j=1 γ j e iφ j t , which has been extensively studied within the last years, see e.g. [16,17,28,2,23,22,25,19,29,18,8,9]. Moreover, there is a close connection to the question of extrapolation of the given sequence of input values (f k ) N −1 k=0 , see e.g.…”

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confidence: 99%

“…At the first glance, the known reconstruction algorithms for exponential sums in [9,11,23,25,26] seem to cover also the problems raised above, since the cosine sum f in (1.1) can be simply transferred into an exponential sum 1 2 M j=1 γ j (e iφ j t + e −iφ j t ), which is just a special case of an exponential sum of length 2M . Indeed, in case of exact measurement data, any reconstruction algorithm for exponential sums can be directly used for the recovery of the parameters of f in (1.1).…”

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confidence: 99%

“…In a recent paper [9], we had proposed an ESPIRA (Estimation of Signal Parameters by Iterative Rational Approximation) algorithm for recovery of exponential sums. As shown in [9], this new method can be successfully applied for reconstruction of exponential sums from noisy data as well as for function approximation, and it essentially outperforms all previous methods in both regards. In Section 3, we now present a new ESPIRA algorithm, which is especially adapted to cosine sums.…”

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confidence: 99%

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ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application

Derevianko¹,

Plonka²,

Razavi³

2022

Preprint

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In this paper we introduce two new algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real positive frequency parameters and therefore strongly generalizes usual Fourier sums. The proposed methods both employ a set of equidistant signal values as input data. The ESPRIT method for cosine sums is a Prony-like method and applies matrix pencils of Toeplitz + Hankel matrices while the ESPIRA method is based on rational approximation of DCT data and can be understood as a matrix pencil method for special Loewner matrices. Compared to known numerical methods for recovery of exponential sums, the design of the considered new algorithms directly exploits the special real structure of the signal model and therefore usually provides real parameter estimates for noisy input data, while the known general recovery algorithms for complex exponential sums tend to yield complex parameters in this case.

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Section: The Arithmetical Complexity Of the Svd Decomposition Of The ...mentioning

confidence: 99%

Section: The Aaa Algorithm For Rational Approximationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application

Derevianko¹,

Plonka²,

Razavi³

2022

Preprint

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HEOM‐QUICK2: A general‐purpose simulator for fermionic many‐body open quantum systems—An update

Zhang,

Ye,

Cao

et al. 2024

WIREs Comput Mol Sci

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Many‐body open quantum systems (OQSs) have a profound impact on various subdisciplines of physics, chemistry, and biology. Thus, the development of a computer program capable of accurately, efficiently, and versatilely simulating many‐body OQSs is highly desirable. In recent years, we have focused on the advancement of numerical algorithms based on the fermionic hierarchical equations of motion (HEOM) theory. Being in‐principle exact, this approach allows for the precise characterization of many‐body correlations, non‐Markovian memory, and non‐equilibrium thermodynamic conditions. These efforts now lead to the establishment of a new computer program, HEOM for QUantum Impurity with a Correlated Kernel, version 2 (HEOM‐QUICK2), which, to the best of our knowledge, is currently the only general‐purpose simulator for fermionic many‐body OQSs. Compared with version 1, the HEOM‐QUICK2 program features more efficient solvers for stationary states, more accurate treatment of non‐Markovian memory, and improved numerical stability for long‐time dissipative dynamics. Integrated with quantum chemistry software, HEOM‐QUICK2 has become a valuable theoretical tool for the precise simulation of realistic many‐body OQSs, particularly the single atomic or molecular junctions. Furthermore, the unprecedented precision achieved by HEOM‐QUICK2 enables accurate simulation of low‐energy spin excitations and coherent spin relaxation. The unique usefulness of HEOM‐QUICK2 is demonstrated through several examples of strongly correlated quantum impurity systems under non‐equilibrium conditions. Thus, the new HEOM‐QUICK2 program offers a powerful and comprehensive tool for studying many‐body OQSs with exotic quantum phenomena and exploring applications in various disciplines.This article is categorized under: Data Science > Computer Algorithms and Programming Software > Simulation Methods Theoretical and Physical Chemistry > Statistical Mechanics

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Prony Method for Reconstruction of Structured Functions

Plonka,

Potts,

Steidl

et al. 2023

Applied and Numerical Harmonic Analysis

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From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation

Cited by 17 publications

References 34 publications

ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application

ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application

HEOM‐QUICK2: A general‐purpose simulator for fermionic many‐body open quantum systems—An update

Prony Method for Reconstruction of Structured Functions

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