Download Convex Optimization for Signal Processing and Communications by Chong-Yung Chi, Wei-Chiang Li, Chia-Hsiang Lin PDF

By Chong-Yung Chi, Wei-Chiang Li, Chia-Hsiang Lin

Convex Optimization for sign Processing and Communications: From basics to Applications presents basic history wisdom of convex optimization, whereas notable a stability among mathematical thought and purposes in sign processing and communications.

In addition to complete proofs and standpoint interpretations for center convex optimization idea, this e-book additionally offers many insightful figures, comments, illustrative examples, and guided trips from conception to state-of-the-art study explorations, for effective and in-depth studying, particularly for engineering scholars and execs.

With the strong convex optimization conception and instruments, this ebook offers you a brand new measure of freedom and the aptitude of fixing difficult real-world medical and engineering problems.

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Extra resources for Convex Optimization for Signal Processing and Communications

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The sum of the projections v1 and v2 uniquely represents the vector x. In other words, the sum of the set V and the set V ⊥ is given by V + V ⊥ = {x + y | x ∈ V, y ∈ V ⊥ } = Rn . 72) are useful properties with regard to the rank of A. 15 A matrix P is said to be an orthogonal projector onto the subspace V = R(P) if and only if P2 = P = PT . For the case that A ∈ Rm×n , the projection matrix for V = R(A) is given by PA = AA† = A AT A Im , −1 AT , if rank(A) = n (cf. 125)) if rank(A) = m (cf. 73) where A† denotes the pseudo-inverse of A (cf.

The sum of the projections v1 and v2 uniquely represents the vector x. In other words, the sum of the set V and the set V ⊥ is given by V + V ⊥ = {x + y | x ∈ V, y ∈ V ⊥ } = Rn . 72) are useful properties with regard to the rank of A. 15 A matrix P is said to be an orthogonal projector onto the subspace V = R(P) if and only if P2 = P = PT . For the case that A ∈ Rm×n , the projection matrix for V = R(A) is given by PA = AA† = A AT A Im , −1 AT , if rank(A) = n (cf. 125)) if rank(A) = m (cf. 73) where A† denotes the pseudo-inverse of A (cf.

VrT Vr = Ir ), and Σ = Diag(σ1 , . . 109) is a rectangular matrix with r positive singular values (supposedly arranged in nonincreasing order), denoted as σi , as the first r diagonal elements and zeros elsewhere. , R(A) = R(Ur ). , sum of r rank-1 matrices ui viT weighted by the associated singular value σi ) where Σr = Diag(σ1 , . . 112) is a diagonal matrix whose diagonal terms σi are the r positive singular values of A. 111)) uTi Avi . 113) Mathematical Background 29 The thin SVD above is computationally more economical than the full SVD.

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