Question

Gradient descent converges after $ T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix

score 239 · Answer 1 · 2026-04-01 01:38:39

239

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Gradient descent converges after $ T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix

Published on 01 Apr 2026 - 1:38

score 81 · Answer 2 · 2021-04-18 18:00:42

81

Views

If $A,B,A-B$ are all symmetric positive definite and real, how to prove that $\forall 0<\alpha<1, A^{\alpha}-B^{\alpha}$ is also positive?

Published on 18 Apr 2021 - 18:00

score 190 · Answer 3 · 2021-04-21 12:58:40

190

Views

Inertia of a quadratic form

Published on 21 Apr 2021 - 12:58

score 46 · Answer 4 · 2021-04-22 04:59:27

46

Views

Don't understand this proof of the maximum principle.

Published on 22 Apr 2021 - 4:59

score 96 · Answer 5 · 2021-04-24 16:30:08

96

Views

symmetric quadratic form on $\mathbb R^3$ and on $\mathbb C^3$

Published on 24 Apr 2021 - 16:30

score 67 · Answer 6 · 2026-03-26 17:53:07

67

Views

Class number of positive definite binary quadratic forms formula

Published on 26 Mar 2026 - 17:53

score 49 · Answer 7 · 2021-04-26 15:14:18

49

Views

Graph Theory in Conway's Topograph

Published on 26 Apr 2021 - 15:14

score 80 · Answer 8 · 2021-04-29 21:59:06

80

Views

Standard quadratic format for objective function

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score 149 · Answer 9 · 2026-03-31 10:02:47

149

Views

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score 680 · Answer 10 · 2021-05-03 03:35:38

680

Views

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Published on 03 May 2021 - 3:35

score 483 · Answer 11 · 2021-05-03 19:26:20

483

Views

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Published on 03 May 2021 - 19:26

score 43 · Answer 12 · 2021-05-04 11:03:49

43

Views

Prove that $\boldsymbol{v}^T\boldsymbol{A}^{-1}\boldsymbol{v}\boldsymbol{z}^T\boldsymbol{A}\boldsymbol{z} \ge (\boldsymbol{v}^T\boldsymbol{z})^2$

Published on 04 May 2021 - 11:03

score 83 · Answer 13 · 2026-04-02 05:28:55

83

Views

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Published on 02 Apr 2026 - 5:28

score 52 · Answer 14 · 2021-05-06 18:27:45

52

Views

Binary quadratic form representing an integer with a vector of level N

Published on 06 May 2021 - 18:27

score 725 · Answer 15 · 2021-05-08 20:26:24

725

Views

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Published on 08 May 2021 - 20:26

List Question

Gradient descent converges after $ T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix

If $A,B,A-B$ are all symmetric positive definite and real, how to prove that $\forall 0<\alpha<1, A^{\alpha}-B^{\alpha}$ is also positive?

Inertia of a quadratic form

Don't understand this proof of the maximum principle.

symmetric quadratic form on $\mathbb R^3$ and on $\mathbb C^3$

Class number of positive definite binary quadratic forms formula

Graph Theory in Conway's Topograph

Standard quadratic format for objective function

Clarification of pseudo-Euclidean space definition

How can we state Sylvester's law of inertia without referring to a particular basis?

Upper bound on quadratic forms

Prove that $\boldsymbol{v}^T\boldsymbol{A}^{-1}\boldsymbol{v}\boldsymbol{z}^T\boldsymbol{A}\boldsymbol{z} \ge (\boldsymbol{v}^T\boldsymbol{z})^2$

Minimum of a quadratic function with mixed nonlinear constraints on a non-convex set.

Binary quadratic form representing an integer with a vector of level N

Classification of a quadratic form

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