Linear Operator Equations - Approximation and Regularization

Nair, M. Thamban

doi:10.1142/9789812835659

Cited by 33 publications

(49 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(8) where I is the L ×L identity matrix and α is a regularization parameter. The choice of α can be obtained using two methods, the L-curve method [13] and the strategy proposed in [14] as will be explained in section 3.3.1 and 3.3.2…”

Section: The Proposed Methodsmentioning

confidence: 99%

See 1 more Smart Citation

An Improved Technique of Channel Estimation for OFDM in DVB-T2

Eldieb¹,

Saleh²,

Elramly³

2014

IJCA

View full text Add to dashboard Cite

Orthogonal Frequency Division Multiplexing (OFDM) with pilot assisted channel estimation is widely applied in wireless communication systems due to its high rate transmission capability and its robustness to multi-path fading and delay. In this paper an improved channel estimation method for OFDM in second generation Digital Video Broadcasting for Terrestrial (DVB-T2) is presented based on a pilot arrangement in time-varying frequency-selective fading channels. A new method which is based on an improved Domain Transform Least Square Estimation method (DTLSE) and a Two Dimensional Interpolation method (2-DI) have been proposed. The proposed methods give a good BER performance compared to other considered methods .The estimation matrix size for obtaining Channel Impulse Response (CIR) depends only on the length of the channel not on the number of pilot subcarriers nor the size of OFDM symbol, it does not require knowledge of channel statistics and works for any pilot pattern. The Minimum Mean Squared Error (MMSE) channel estimation was considered as the reference method that gives the best BER performance but suffers from a high computational load. The proposed method is compared with the two other methods: the improved DTLSE and MMSE. The proposed method proves to give a reduction in complexity compared to the MMSE technique with a comparable performance but better than the DTLSE one.

show abstract

Section: The Proposed Methodsmentioning

confidence: 99%

“…Another strategy proposed in [14] is used in which the expression of α given for pilots amplitude-boosted ( and SNR as (13) …”

Section: Mathematical Methodsmentioning

confidence: 99%

An Improved Technique of Channel Estimation for OFDM in DVB-T2

Eldieb¹,

Saleh²,

Elramly³

2014

IJCA

View full text Add to dashboard Cite

show abstract

“…(See Remarks 3.10 and 3.12, and Theorem 3.24 of [11]). We thus note that existence and convergence of approximate solutions to the exact solution of an operator equation is guaranteed under the norm convergence of the sequence (T n ) to T , but not under the pointwise convergence of (T n ) to T .…”

Section: − → T and Z ∈ ρ(T )mentioning

confidence: 98%

Operator Approximation

Limaye¹

2015

Semigroups, Algebras and Operator Theory

View full text Add to dashboard Cite

We present an introduction to operator approximation theory. Let T be a bounded linear operator on a Banach space X over C. In order to find approximate solutions of (i) the operator equation z x − T x = y, where z ∈ C and y ∈ X are given, and (ii) the eigenvalue problem T ϕ = λϕ, where λ ∈ C and 0 = ϕ ∈ X , one approximates the operator T by a sequence (T n ) of bounded linear operators on X . We consider pointwise convergence, norm convergence, and nu convergence of (T n ) to T . We give several examples to illustrate possible scenarios. In most classical methods of approximation, each T n is of finite rank. We give a canonical procedure for reducing problems involving finite rank operators to problems involving matrix computations.

show abstract

“…The kernel Ker(I) of I is closed in H so that, for any y ∈ R n ,ȟ = I † (y) is the unique solution of (Q), where I † is the generalized inverse or Moore-Penrose inverse of I (see [21]). If the matrix K = K x (i) , x …”

Section: Introductionmentioning

confidence: 99%