Fast QR factorization of Vandermonde matrices

Demeure, C.J.

doi:10.1016/0024-3795(89)90652-6

Cited by 40 publications

(18 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although numerical algorithms for the solution of (ordinary) Vandermonde systems are known [19,20] r ~ 2M + 1, consequently the system matrix has always full rank, independent of the sampling geometry. This is no longer true in higher dimensions.…”

Section: Trigonometric Polynomialsmentioning

confidence: 99%

Numerical and Theoretical Aspects of Nonuniform Sampling of Band-Limited Images

Gröchenig

Strohmer

2001

Nonuniform Sampling

View full text Add to dashboard Cite

6This chapter presents recent developments and progress in nonuniform sampling of band-limited functions. Since the theory and practice of nonuniform sampling of I-D signals are well understood and already treated in many articles and surveys, the emphasis will be on the nonuniform sampling of images. Both numerical, theoretical, and applied aspects of the sampling problem will be considered. For Matlab© simulations, see the CD-ROM: 'Chapter6\matlab'. 6

show abstract

Section: Trigonometric Polynomialsmentioning

confidence: 99%

Numerical and Theoretical Aspects of Nonuniform Sampling of Band-Limited Images

Gröchenig

Strohmer

2001

Nonuniform Sampling

View full text Add to dashboard Cite

show abstract

“…On the other hand, we know that System (7) can be written as Vandermonde matrices and solved by the Vandermonde least square methods as in [27][28][29]. The order of complexities of these methods is O((J 1)NL+L 2 ), whereas the complexity order of the proposed technique is O(L 2 ).…”

Section: Complexity Analysismentioning

confidence: 99%

“…For a reasonable PAPR value, the number of clipped samples is usually much less than the total number of out-of-band components, i.e. L << (J 1)N. Therefore, the complexity order of the proposed solution is less than those of [27][28][29].…”

Section: Complexity Analysismentioning

confidence: 99%

Amplitude reconstruction of clipped OFDM by using DFT-based least squares

Ahmadi

Talebi

2017

Scientia Iranica

View full text Add to dashboard Cite

Abstract. OFDM is an e ective multicarrier transmission technique with one primary disadvantage; it su ers from high Peak-to-Average Power Ratio (PAPR). Although clipping and ltering is a simple and e ective method for PAPR reduction, it makes in-band and out-of-band noise, which degrades the bit error rate performance and spectral e ciency. Publications on this subject show that clipped samples could be reconstructed at the receiver by using oversampled signal and bandwidth expansion. By building on published literature, this paper aims to achieve a low-complexity method. The proposed method has complexity order of O(L 2 ) to solve linear system, where L indicates the number of clipped samples. Simulation results con rm that our proposed method leads to both a better biterror rate performance and a lower complexity than similar methods. These results also show that our method o ers adequate performance, especially at low clipping ratios.

show abstract

“…Rectangular Vandermonde matrices on general nodes have been considered in [3], where fast algorithms for the Cholesky factorization of the normal matrix B = V T V and for the QR factorization of V are given.…”

Section: Introductionmentioning

confidence: 99%