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Sparse Polynomial Approximation of High-Dimensional Functions
Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions.These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data.This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods.These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations.It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing.It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code.The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
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Essens chrome cantilever frame and leather faced seat and back offers a sophisticated style with a hint of retro. Available in black and grey with matching padded arms, the smoothly shaped seat and back gently cradle and support the body, providing
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Essen Electric Leather Recliner 3 Seater Sofa In Black
Essen Electric Leather Recliner 3 Seater Sofa in Black, a pinnacle of comfort and sophistication exclusively from Furniture in Fashion. Crafted with meticulous attention to detail, this sofa seamlessly blends premium leather upholstery with modern design elements. The timeless black color adds a touch of elegance to any living space while offering versatility in styling. Equipped with an electric reclining mechanism, this sofa ensures effortless adjustment to your desired position, providing personalized comfort with just the touch of a button. Whether placed in a formal living room or a cozy lounge area, the Essen Electric Leather Recliner 3 Seater Sofa promises to elevate the ambiance of your home with its luxurious design and superior functionality. FEATURES : Material : Full Leather Finish : Black Full Leather / Leather Match Lumbar Support with High Headrest Full Electric Recliner Push Button Mechanism with USB charging port Black leather upholstery exudes sleekness and modernity Electric recliner mechanism provides customizable comfort effortlessly Crafted with premium leather for durability and lasting quality Essen style adds a contemporary touch to any living space Ideal for accommodating guests or lounging with family in style Elevate your home dcor with the sleek Essen Electric Leather Recliner 3 Seater Sofa in Black Available at an affordable price Images shown are for illustration purpose only DIMENSIONS : Height : 105cm Width : 80cm Length : 205cm
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What is the difference between a polynomial and a polynomial function?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or roots. A polynomial function, on the other hand, is a specific type of function that can be defined by a polynomial expression. In other words, a polynomial function is a function that can be expressed as a polynomial. So, while a polynomial is simply an algebraic expression, a polynomial function is a specific type of mathematical function.
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What are polynomial functions?
Polynomial functions are mathematical functions that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. These functions can have multiple terms, each with a different power of the variable. Polynomial functions are continuous and smooth, and they can be used to model a wide range of real-world phenomena. They are commonly used in algebra, calculus, and other branches of mathematics to analyze and solve various problems.
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What is double polynomial division?
Double polynomial division is a method used to divide one polynomial by another polynomial. It involves dividing the leading term of the dividend by the leading term of the divisor to determine the first term of the quotient. This process is repeated for each subsequent term until the entire dividend is divided by the divisor. The result is a quotient and a remainder, if any.
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What is a polynomial space?
A polynomial space is a vector space whose elements are polynomials. In other words, it is a set of all polynomials of a certain degree, along with the operations of addition and scalar multiplication. The dimension of a polynomial space is determined by the highest degree of the polynomials in the space. Polynomial spaces are commonly used in mathematics and engineering to represent and manipulate functions and data.
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Fear Eats the Soul (Angst Essen Seele Auf)
In Rainer Werner Fassbinder's Fear Eats the Soul (Angst Essen Seele Auf, 1974) Emma (Brigitte Mira), a working-class widow and former member of the Nazi party, marries Ali (El Hedi ben Salem), a much younger Moroccan migrant worker.Set in Munich during the 1970s, the film melds the conventions of melodrama with a radical sensibility to present a portrait of racism and everyday hypocrisy in post-war Germany.It is a film about the way conventional society detests anything and anybody unfamiliar - but also a film about the hopes and limits of love.Intricately directed, beautifully performed, and designed to show Munich life in all its shabby kitschiness, Fear Eats the Soul may be Fassbinder's finest film. Laura Cottingham celebrates Fassbinder's achievement, placing Fear Eats the Soul in relation to his extraordinarily prolific career in theatre, film and television.Her analysis pulls back the thin curtain that separated his work from his tumultuous life.She also explores the director's debt to the lush Hollywood melodramas made by fellow German Douglas Sirk, especially All That Heaven Allows (1955).In a detailed scene-by-scene analysis, Cottingham shows how Fassbinder managed to combine beauty and tenderness with fierce political critique.
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Essen Wooden Mid Sleeper Single Bunk Bed In White
Essen Wooden Mid Sleeper Single Bunk Bed in White is a vEssentile and space-saving addition to your child's or teenager's bedroom, thoughtfully designed by Furniture in Fashion. This mid-sleeper bed combines modern design with functionality, making it an excellent choice for smaller spaces. The bed frame is finished in clean and crisp white, adding a fresh and neutral look to the room. What sets this bed apart is the raised sleeping platform, which allows you to utilize the space underneath for various purposes. You can create a cozy study area, play space, or storage space, making it a practical and vEssentile solution for smaller bedrooms. Elevate your child's or teenager's bedroom with the Essen Wooden Mid Sleeper Single Bunk Bed, where style and functionality merge seamlessly, creating a well-organized and multifunctional sleeping and living space. Experience the convenience of maximizing space while maintaining a modern and organized room with this thoughtfully designed bed from Furniture in Fashion. FEATURES : Material : Solid Rubberwood Finish : White Ladder offers easy access with handholds Solid Rubberwood and superior quality materials Features multiple storage options and nondetachable desk Shelving unit with 3 shelves and built-in shelving Cabinet and desk can be used anywhere Comprehensive instructions included Shelving unit shelves are 33cm high and 38. 5cm deep Top shelf is 93cm wide and bottom two are 45. 75cm wide Available at an affordable price Images shown are for illustration purpose only DIMENSIONS : Height : 140. 7cm Width : 131. 6cm Length : 196. 6cm Cabinet with 3 Pull-Out Drawers : L89cm x W40cm x H75. 5cm Each Drawer Internal Size : L79. 5cm x D33. 8cm x H12. 9cm Spacious Pull-Out Desk : L93cm x W60cm x H70cm Small Shelves at the back : H20cm x L63. 5cm
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Essen Electric Leather Recliner 1 Seater Sofa In Black
Essen Electric Leather Recliner 1 Seater Sofa in Black, an epitome of comfort and sophistication exclusively from Furniture in Fashion. Expertly crafted with premium leather, this sofa embodies both elegance and durability. The timeless black color adds a touch of refinement to any room while offering a versatile aesthetic. Equipped with an electric reclining mechanism, this sofa offers effortless adjustment to your desired position, ensuring personalized comfort at the touch of a button. Whether placed in a cozy reading nook or as a statement piece in your living room, the Essen Electric Leather Recliner 1 Seater Sofa promises to elevate the ambiance of your home with its luxurious design and superior functionality. FEATURES : Material : Full Leather Finish : Black Full Leather / Leather Match Lumbar Support with High Headrest Full Electric Recliner Push Button Mechanism with USB charging port Black leather upholstery exudes sleekness and modernity Electric recliner mechanism provides customizable comfort effortlessly Crafted with premium leather for durability and lasting quality Essen style adds a contemporary touch to any living space Ideal for smaller living areas or as an accent piece Elevate your home dcor with the stylish Essen Electric Leather Recliner 1 Seater Sofa in Black Available at an affordable price Images shown are for illustration purpose only DIMENSIONS : Height : 105cm Width : 80cm Length : 105cm
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Is 2x a polynomial function?
Yes, 2x is a polynomial function. A polynomial function is a function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. In the case of 2x, it can be written as 2x^1, which fits the definition of a polynomial function.
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"Is my polynomial function correct?"
To determine if your polynomial function is correct, you should first check if it satisfies the given conditions or constraints. Then, you can verify if the function produces the expected output for a range of input values. Additionally, you can compare your function with other known correct polynomial functions to see if they match. If your function meets all these criteria, it is likely correct. However, it's always a good idea to double-check your work and seek feedback from others to ensure accuracy.
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What is the polynomial form?
The polynomial form is a mathematical expression consisting of variables, coefficients, and exponents. It is a sum of terms, where each term is a variable raised to a non-negative integer power, multiplied by a coefficient. The polynomial form is used to represent various mathematical functions and equations, and it can be manipulated through operations such as addition, subtraction, multiplication, and division. The degree of a polynomial is determined by the highest exponent of the variables present in the expression.
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What is a constant polynomial?
A constant polynomial is a polynomial function that has a degree of zero, meaning it does not contain any variables. It is simply a constant value, such as 5 or -3. Constant polynomials are represented in the form f(x) = c, where c is a constant value. These polynomials do not change in value as x varies, hence the term "constant."
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