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  • [數] 奇異值分解

  • 例句

  • The discrete model of the thermal dynamics process of precision machine was used to establish a new method called singular value decomposition algorithm for identifying these characteristics.

    在精密機械熱動态過程的離散化模型基礎上,提出一種識别精密機械熱動态特性參數的新方法——奇異值分解算法。

  • Fractal singular value neighbor distance is brought forward based on fractal neighbor distance. Fractal coding and local singular value decomposition are used to improve the recognition rate.

    在分形近鄰距離的基礎上,提出了分形奇異值近鄰距離,并把分形編碼和局部奇異值分解結合起來,提高了識别率。

  • Low-rank estimation used the frequency correlation of the channel and singular value decomposition method.

    低秩估計方法利用信道的頻域(/時域)關性以及奇異值分解技術。

  • A robust stability boundary of uncertain singular systems is proposed by utilizing singular value decomposition and the character of mode matrix.

    并利用奇異值分解方法和模矩陣的性質,給出了使不确定廣義系統魯棒穩定的一個魯棒界。

  • And a method using iterative singular value decomposition (SVD) was presented for reducing the noise from a nonlinear time series to yield an improvement in the correlation dimension estimation.

    采用疊代奇異值分解算法對含噪聲的信號進行降噪,降低了噪聲對相關維數計算結果的影響,從而提高了計算結果的可靠性。

  • An approach of suppressing the transient interference based on Singular Value Decomposition (SVD) is presented in this paper.

    該文提出了基于矩陣奇異值分解的高頻雷達瞬态幹擾抑制方法。

  • In addition, a method based on singular value decomposition(SVD) was proceed to deal with the obtained result for dropping influence of noise.

    為降低噪聲的影響,采用一個基于奇異值分解(SVD)的方法對識别的結構進行處理。

  • In order to solve these problems, a rank-truncated multi-station TDOA localization algorithm based on singular value decomposition was presented.

    為了解決這些問題,提出了一種基于奇異值分解的秩截短多站時差定位算法。

  • The Singular Value Decomposition (SVD) method for the equilibrium matrix is developed and a physical explanation is given.

    引入了平衡矩陣的奇異值分解(SVD)方法并解釋了其力學含義。

  • The problem of image matching and target tracking based on singular value decomposition (SVD) was discussed.

    研究了基于奇異值分解的圖像匹配和目标跟蹤問題。

  • Singular Value Decomposition (SVD) is a dimension reduction method, and Symbolic Data Analysis (SDA) is a new analytical approach to processing mass data.

    奇異值分解(SVD)是一種對數據進行降維處理的方法,符號數據分析(SDA)是一種處理海量數據的全新數據分析思路。

  • And by the reduction of pilot numbers, frequency resource of the system is increased. In addition, with singular value decomposition, the algorithm computational complexity can be simplified.

    通過簡化導頻數提高了系統頻帶利用率,利用奇異值分解進一步簡化了算法複雜度。

  • Feature points' 3D coordinates are computed through singular value decomposition of projector matrix, then compute projector matrix by triangulation.

    對應特征點的三維重建是根據三角測量的方法計算其投影矩陣,然後用奇異值分解求出特征點的三維齊次坐标。

  • To visualize the high dimension ellipsoidal RA approximately, a novel projection approach based on singular value decomposition for high dimension ellipsoidal RA is proposed in multi-machine case.

    在多機系統中,應用奇異值分解方法,提出了高維橢球吸引域的三維投影方法,解決了高維橢球吸引域的直觀顯示問題。

  • Then, by the generalized singular value decomposition, a general symmetric solution of the minimum residual problem is obtained.

    主要給出了矩陣的最小剩餘問題及其最優近似問題的對稱解。

  • A subspace-based tracking algorithm is proposed for high-resolution DOA estimation, using the generalized singular value decomposition (GSVD) of the sample data matrices.

    本文論述了一種基于子空間方法的高分辨DOA估計跟蹤問題的解法。

  • Statistical Process Control (SPC), Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) are introduced to det ermine APC opportunity and then APC structure.

    這一研究對于開發和應用好先進控制技術具有重要的意義。

  • A novel method based on Bilateral Two-Dimensional Linear Discriminant Analysis(B-2DLDA) and symmetry average of local Singular Value Decomposition(SVD) for face recognition is presented.

    針對人臉識别中光照、表情、姿态的影響,提出一種融合雙向二維線性鑒别分析和局部對稱平均的人臉識别新方法。

  • An algorithm for vehicle license plate tilt correction base on singular value decomposition;

    該文提出基于字符投影點坐标方差最小的車牌垂直傾斜校正方法。

  • In this paper, an approach of soft-faults diagnosis based on characteristics extraction with singular-value decomposition (SVD) is presented.

    利用奇異角特征方法能減少測試點數、壓縮特征矢量維數和提高故障隔離率。

  • 專業解析

    奇異值分解(Singular Value Decomposition, SVD)是線性代數中一種重要的矩陣分解方法,廣泛應用于信號處理、數據降維和機器學習等領域。給定任意( m times n )的實數或複數矩陣( A ),其分解形式為:

    $$ A = U Sigma V^T $$

    其中:

    核心特性與意義

    1. 數據降維:通過保留前( k )個最大的奇異值,可實現矩陣的低秩近似,常用于圖像壓縮和主成分分析(PCA)。
    2. 數值穩定性:奇異值反映了矩陣的“能量分布”,較大的奇異值對應數據中的主要特征,較小的可能代表噪聲。
    3. 解線性方程組:在最小二乘問題和病态方程求解中,SVD通過截斷小奇異值提升解的穩定性。

    應用領域

    參考來源:

    1. MIT線性代數公開課(鍊接
    2. 《Numerical Linear Algebra》(Trefethen & Bau)
    3. MathWorld數學百科(鍊接
    4. IEEE信號處理期刊(鍊接

    網絡擴展資料

    奇異值分解(Singular Value Decomposition,SVD)是一種重要的矩陣分解方法,廣泛應用于線性代數、數據科學和機器學習領域。以下是詳細解釋:

    1.定義與數學形式

    SVD将任意實數或複數矩陣 ( A )(( m times n ) 維)分解為三個特定矩陣的乘積: $$ A = U Sigma V^T $$

    2.幾何意義

    SVD揭示了矩陣的幾何結構:

    3.關鍵性質

    4.應用場景

    5.計算示例

    假設矩陣 ( A ) 為: $$ A = begin{bmatrix} 1 & 23 & 4 end{bmatrix} $$ 其SVD分解結果為:

    SVD通過分解矩陣到其“核心成分”,提供了一種分析數據結構和降維的通用工具。其數學優雅性和實用性使其成為現代科學計算的基石之一。

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