Adverbs of Change

Koev, Todor

doi:10.1007/978-3-030-04438-1_14

Cited by 6 publications

(21 citation statements)

References 29 publications

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“…In practice, the constant hidden by the big-O notation (for time complexity) is greatly increased when computing indices on the fly; therefore, since n N we have found the lookup table approach to be much more efficient. Further discussion of implementation issues and MATLAB code for both methods are available online [21].…”

Section: The First Algorithmmentioning

confidence: 99%

On computing Schur functions and series thereof

et al. 2018

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Section: The First Algorithmmentioning

confidence: 99%

On computing Schur functions and series thereof

et al. 2018

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“…We provide a detailed error analysis of the truncated series in Section 4.3. MATLAB implementations of Koev and Edelman's algorithms are available in the author's homepage [25]. But the routine gets only real eigenvalues as input arguments.…”

Section: Sampling From the Conditional Distribution Of Y T Given X Tmentioning

confidence: 99%

Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model

Kang¹,

Kang

Lee³

2017

Operations Research

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In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. [14]. Our method is based on analysis of the conditional characteristic function of the logprice given volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. We perform numerical experiments to demonstrate the performance and accuracy of our method. As a result of numerical experiments, it is shown that our new method is much faster and reliable than Euler discretization method.

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“…Step 2 can be carried out by using the algorithm TNSolve of P. Koev [19]. Given the bidiagonal factorization of the matrix A, TNSolve solves Ax = b by using backward substitution.…”

Section: Linear System Solvingmentioning

confidence: 99%

“…TNEigenvalues is an algorithm of P. Koev [20] which computes accurate eigenvalues of a totally positive matrix starting from its bidiagonal factorization. The computational cost of TNEigenvalues is of O(n 3 ) arithmetic operations (see [20]) and its implementation in Matlab can be taken from [19]. In this way, as the computational cost of Step 1 is of O(n 2 ) arithmetic operations, the cost of the whole algorithm is of O(n 3 ) arithmetic operations.…”

Section: Inputmentioning

confidence: 99%

“…TNSingularValues is an algorithm of P. Koev that computes accurate singular values of a totally positive matrix starting from its bidiagonal factorization [20]. Its computational cost is of O(n 3 ) and its implementation in Matlab can be found in [19]. Taking this complexity into account, the computational cost of our algorithm for computing the singular values of a totally positive Cauchy-Vandermonde matrix is of O(n 3 ) arithmetic operations.…”

Section: Inputmentioning

confidence: 99%

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Accurate bidiagonal decomposition of totally positive Cauchy–Vandermonde matrices and applications

Marco

Martínez

Peña

2017

Linear Algebra and its Applications

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Cauchy-Vandermonde matrices play a fundamental role in rational interpolation theory and in other fields. When all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings, these matrices are totally positive. In this paper we provide fast algorithms for computing bidiagonal factorizations of these matrices and their inverses with high relative accuracy. These algorithms can be used to solve with high relative accuracy other algebraic problems, such as the computation of all singular values, all eigenvalues or the solution of certain linear systems. The error analysis of the algorithm for computing the bidiagonal factorization and the corresponding perturbation theory are also performed.

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Adverbs of Change

Cited by 6 publications

References 29 publications

On computing Schur functions and series thereof

On computing Schur functions and series thereof

Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model

Accurate bidiagonal decomposition of totally positive Cauchy–Vandermonde matrices and applications

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