克利夫角:克利夫·莫尔谈数学和计算机 https://blogs.mathworks.com/cleve Cleve Moler是第一个MATLAB的作者,MathWorks的创始人之一,目前是该公司的首席数学家。他在这里写了MATLAB,科学计算和有趣的数学。 太阳,2021年10月3日14:57:10 +0000 恩美 每小时 1 https://wordpress.org/?v=4.9.15 马修/摩尔 https://feedburner.google.com 计算机图形矩阵与立方体 http://feedproxy.google.com/~r/mathworks/moler/~3/a4kMLu9E5uw/ https://blogs.mathworks.com/cleve/2021/10/03/the-computer-graphics-matrix-and-a-cube/#respond 2021年10月3日星期日14:42:11+0000 克里夫·莫勒尔 颜色 享乐 图样 矩阵 https://blogs.mathworks.com/cleve/?p=7488

Use a cube instead of the Utah Teapot in my previous post. I was pleasantly suprised by the final screen shot.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " http://blogs.mathworks.com/cleve/files/grafix_cube_2_01.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“/>

Use a cube instead of the Utah Teapot in my previous post. I was pleasantly suprised by the final screen shot.

ContentsRGB cubeRzRx*RzRz*RxRyTxSxyzAll togetherClippedWhich?RGB cube

Three faces of our cube are colored with red, green and blue. The opposite faces have the complentary colors, cyan, magenta and

...read more >>

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计算机图形学的核心矩阵 http://feedproxy.google.com/~r/mathworks/moler/~3/OmQdm4qTP2Q/ https://blogs.mathworks.com/cleve/2021/10/03/the-matrix-at-the-heart-of-computer-graphics/#comments 太阳,2021年10月3日10:50:26 +0000 克里夫·莫勒尔 享乐 图样 矩阵 https://blogs.mathworks.com/cleve/?p=7449

Matrices like the ones shown in the following screen shots are at the heart of computer graphics. They describe objects moving in three-dimensional space. MATLAB's Handle Graphics uses them. So does MathWork's new RoadRunner editor. And so do all popular video games and CAD packages.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " http://blogs.mathworks.com/cleve/files/grafix_heart_blog_01.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“如下屏幕截图所示的矩阵是计算机图形学的核心。They describe objects moving in three-dimensional space. MATLAB's Handle Graphics uses them. So does MathWork's new RoadRunner editor. And so do all popular video games and CAD packages.

ContentsUtah TeapotMRotationRz*RxRyTranslation and scalingAll togetherUtah Teapot

From its introduction in 1976 by Martin Newell, then a grad student at the University of Utah, the Teapot has played an import role in the

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四元数 http://feedproxy.google.com/~r/mathworks/moler/~3/OiV6t9hcdPI/ https://blogs.mathworks.com/cleve/2021/09/06/quaternions/#comments 2021年9月6日星期一11:28:53+0000 克里夫·莫勒尔 算法 图样 历史 编程 四元数 https://blogs.mathworks.com/cleve/?p=7255
<!”--简介-->

四元数是复数的推广,在计算机图形学和许多其他领域都有应用阅读更多>>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " http://blogs.mathworks.com/cleve/files/grafix_heart_blog_01.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“/>

四元数是在计算机图形学和许多其他领域发现应用的复数的概括。内容< / p > < a href = " # 8 aaa90c7 - 8166 - 4325 - b670 d71ff40c423a”> Ed天使< / > < a href = " # 744 b6e76 - 6汇集4747 - bae0 d074aecab3e5”>两个维度< / > < a href = " # 74 ca6370 - 28 - e2 - 417 f - bc3c - 5013826 - b6572”>三维< / > < a href = " # 419 ccb86-4cc1-49f1-a4cd-8ef22b090470 " >威廉·罗文汉密尔顿< / > < a href = " # 1 d92ae82 - 9322 - 4521 - bbab - 11 - a54b86c295”>点和交叉s manbetx 845产品< / > < a href = " # a09fb4e2-8d61-42a7-8f38-2c013e056c7c " >四元数< / > < a href = " # 6 c249cb2 - 5 - c3e - 4880 -贝科- 63430 - e62fb44”>四元数增加< / > < a href = " # 3 f7e0caf - 9 - c8c - 448 a - 9316 e94374533e1a”>四元数乘法< / > < a href = " # e91db608 b9c9 - 4 - e5f a7d2 - 89 aded68fd12”>美中不足科学< / > < a href = " # 7 cac949e - 0 - e12汽油- 4 - d48 aa85 - 122 e0ae9b36c”>本考察团< / > < / > < a href = " # 801387 d2 - da2c - 4 - aa8 - 8535 - 429 - d814c8769”>随机< / > < a href = " # b8a4c856 - 760 - b - 455 - c - 8630 - 70 - d7850c53fc " > < / > <旋转一个< / p > < p >…read more >>

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圆形,带拉杆断路器,原型 http://feedproxy.google.com/~r/mathworks/moler/~3/vNUGUC9AV6w/ 太阳,2021年7月25日14:18:41 +0000 克里夫·莫勒尔 历史 数值分析 精度 https://blogs.mathworks.com/cleve/?p=7241

In February and March I published three blog posts about an enhancement request for MATLAB concerning tie breakers with the round function, including the ability to round ties to even. Round One, Round Two and Round Three. Since then, a group of us at MathWorks, organized by my colleague (and academic great-great-grand-descendant) Heiko Weichelt, have been considering the request. We had a virtual design review recently. This post describes a prototype incorporating the features that were discussed at that review.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width:500px;" src="//www.tianjin-qmedu.com/blogs/cleve/files/round_proto_blog_01.png" onError="this.onerror=null; this.src='https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg';" />

In February and March I published three blog posts about an enhancement request for MATLAB concerning tie breakers with the round function, including the ability to round ties to even. Round One, Round Two and Round Three. Since then, a group of us at MathWorks, organized by my colleague (and academic great-great-grand-descendant) Heiko Weichelt, have been considering the request. We had a virtual design review recently. This post describes a prototype incorporating the features that were discussed at that review.

Contentsroundfloor and ceilTies

...read more >>

https://blogs.mathworks.com/cleve/2021/07/25/round-with-tie-breakers-a-prototype/?s_tid=feedtopost
我所知道的计算机 http://feedproxy.google.com/~r/mathworks/moler/~3/YNWbqoWO6Gg/ 星期三,7月7日13:00:56 +0000 克里夫·莫勒尔 历史 https://blogs.mathworks.com/cleve/?p=7181

Nick Higham's Numerical Linear Algebra group at the University of Manchester is hosting a conference celebrating Jack Dongarra's 70th birthday July 7 and 8. I am giving a talk, virtually, on July 7. I plan to reminisce about how I did computing in the days before everybody had their own computer in their lap. Here are the slides for the talk, some notes, and some links to this blog for more details.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width:500px;" src="//www.tianjin-qmedu.com/blogs/cleve/files/round_proto_blog_01.png" onError="this.onerror=null; this.src='https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg';" />

Nick Higham's Numerical Linear Algebra group at the University of Manchester is hosting a conference celebrating Jack Dongarra's 70th birthday July 7 and 8. I am giving a talk, virtually, on July 7. I plan to reminisce about how I did computing in the days before everybody had their own computer in their lap. Here are the slides for the talk, some notes, and some links to this blog for more details.

These computers that have been a vital part of my professional life.

ContentsCaltech and University of Utah, 1959 and 1960Jet Propulsion Laboratory, 1960 - 1961Used punched cards.Stanford, 1961 - 1965ETH

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https://blogs.mathworks.com/cleve/2021/07/07/computers-that-i-have-known/?s_tid=feedtopost
计算对称矩阵特征值的复杂性 http://feedproxy.google.com/~r/mathworks/moler/~3/0McgX4pHbkA/ https://blogs.mathworks.com/cleve/2021/05/26/complexity-of-computing-the-eigenvalues-of-a-symmetric-matrix/#comments 5月26日星期三11:37:24 +0000 克里夫·莫勒尔 算法 特征值 历史 矩阵 数值分析 https://blogs.mathworks.com/cleve/?p=7106

I am giving a five-minute talk today, May 26, at the virtual seminar on Complexity of Matrix Computations. Here are my slides. Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in symeig.m.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " http://blogs.mathworks.com/cleve/files/symeig_01.jpg " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“/>

I am giving a five-minute talk today, May 26, at the virtual seminar on Complexity of Matrix Computations. Here are my slides. Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in symeig.m.

Contentssymeig_01symeig_02symeig_03symeig_04symeig_05symeig_06symeig_01 imshow('symeig_01.jpg') symeig_02 imshow('symeig_02.jpg') symeig_03 imshow('symeig_03.jpg')

...read more >>

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对称矩阵特征值的计算 http://feedproxy.google.com/~r/mathworks/moler/~3/zchnBQNsfA0/ https://blogs.mathworks.com/cleve/2021/05/25/computing-eigenvalues-of-symmetric-matrices/#comments 5月26日星期三00:06:40 +0000 克里夫·莫勒尔 特征值 历史 矩阵 数值分析 https://blogs.mathworks.com/cleve/?p=7046

Computing Eigenvalues of Symmetric MatricesSee revision.Get the MATLAB code (requires JavaScript) Published with MATLAB®... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“/>

Computing Eigenvalues of Symmetric Matrices

See revision.


Get the MATLAB code (requires JavaScript)

Published with MATLAB®


...read more >>

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把爆球带回来 http://feedproxy.google.com/~r/mathworks/moler/~3/CUdcs0FmPjM/ 2021年5月12日星期三20:16:36+0000 克里夫·莫勒尔 享乐 图样 历史 https://blogs.mathworks.com/cleve/?p=6954

The Bucky Ball provides an elegant example of a graph, the connectivity of the Buckminster Fuller geodesic dome.We are also demonstrating publishing this blog with the Live Editor. There is a button... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " https://blogs.mathworks.com/cleve/files/BuckyBall_1.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“Bucky Ball提供了一个优美的图形示例,即Buckminster Fuller测地线圆顶的连通性。We are also demonstrating publishing this blog with the Live Editor. There is a button at the end of the post that downloads the live script so that you can run the animation on your own computer. You may see a second button at the end of the post that allows the live script to be executed by MATLAB Online and the results displayed in your browser. This feature is still under development and does not work in some browsers.BuckyThe statement B = bucky; creates a sparse 60-by-60 matrix, the adjacency matrix of the connectivity graph for a geodesic dome, a soccer ball, a carbon-60 molecule or a truncated icosahedron. These objects all have 32 faces; 12 of them are pentagons and 20 are hexagons. SpyOne view of this matrix is its spy plot, which shows the logical structure of nodes and edges. spy(B)GraphTo get other views, use the MATLAB graph object. The statement G

...read more >>

https://blogs.mathworks.com/cleve/2021/05/12/bringing-back-the-bucky-ball/?s_tid=feedtopost
求解广义线性系统 http://feedproxy.google.com/~r/mathworks/moler/~3/m_cIlumE96Q/ https://blogs.mathworks.com/cleve/2021/04/28/solving-commodious-linear-systems/#comments Thu, 29 Apr 2021 00:13:13 +0000 克里夫·莫勒尔 矩阵 数值分析 编程 奇异值 https://blogs.mathworks.com/cleve/?p=6884
<!”--简介-->

这是关于方程少于变量的线性系统A*x=b其中m-by-n矩阵A的行数少于列数,因此m<;n。我总是把这样的系统称为“宽”或“胖”,但这是不礼貌的。因此,我查阅了《韦氏词典》,找到了宽敞的阅读更多>>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " https://blogs.mathworks.com/cleve/files/BuckyBall_1.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“/>

This is about linear systems with fewer equations than variables; A*x = b where the m -by- n matrix A has fewer rows that columns, so m < n . I have always called such systems wide or fat, but this is not respectful. So I consulted the Merriam-Webster Thesaurus and found commodious.

This is also one my first posts to use the Live Editor™. Here is a a link to the .mlx file.

ContentsCommodious linear systemsGenerate examplesBackslashPseudoinverseSVDQuestions

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复活节和愚人节 http://feedproxy.google.com/~r/mathworks/moler/~3/m5H-NfYDPOg/ https://blogs.mathworks.com/cleve/2021/04/08/easter-sunday-and-april-fools/#comments 星期五,09 Apr 2021 01:36:43 +0000 克里夫·莫勒尔 算法 享乐 历史 编程 https://blogs.mathworks.com/cleve/?p=6873

What do the years 2018, 2029 and 2040 have in common? They are the only years in the 21st century when Easter Sunday occurs on April Fools Day.... read more >>

< div > < img风格= "显示:块;保证金:汽车;max-width: 500 px; " src = " http://blogs.mathworks.com/cleve/files/easter_blog_01.png " onError = " this.onerror =零;this.src = ' https://blogs.mathworks.com/wp-content/themes/mathworks_1.0/images/placeholder_9.jpg ';“2018年、2029年和2040年有什么共同之处?这是21世纪唯一的一年,复活节在4月愚人节。

ContentsFool Meets Bunny21st CenturyEaster DayEaster functionFool Meets Bunny for y = 1:100 april_first = datenum(y+2000,4,1); delta(y) = easter(y+2000) - april_first; end years = 2000 + find(delta == 0) years = 2018 2029 2040 21st Century

This plot shows the April Fools Easter Sundays in the 21st century and also shows that Easter can occur on any date between March 22 between April 25.

p = plot(delta,'.'); annotate(p,delta) Easter Day

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